(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 6.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[    132737,       3607]
NotebookOptionsPosition[    130249,       3518]
NotebookOutlinePosition[    130591,       3533]
CellTagsIndexPosition[    130548,       3530]
WindowFrame->Normal
ContainsDynamic->False*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Derivation of CC-R12 equations", "Title"],

Cell["Setup", "Subtitle"],

Cell["Definitions", "Subsubtitle"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"One", "-", 
      RowBox[{
      "particle", " ", "indices", "\[IndentingNewLine]", "named", " ", 
       "indices", " ", 
       RowBox[{"(", 
        RowBox[{"i", ",", "j", ",", "..."}], ")"}], " ", "are", " ", "for", 
       " ", "external", " ", "symbols", " ", "only", "\[IndentingNewLine]", 
       "internal", " ", "symbols", " ", "are", " ", "defined", " ", "by", " ",
        
       SubscriptBox["o", "1"]}]}], ",", " ", 
     RowBox[{"etc", "."}]}], "\[IndentingNewLine]", "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"i", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<i\>\"", ",", "occ"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"j", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<j\>\"", ",", "occ"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"k", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<k\>\"", ",", "occ"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"l", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<l\>\"", ",", "occ"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"m", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<m\>\"", ",", "occ"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"n", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<n\>\"", ",", "occ"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["i", "1"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(i\), \(1\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["j", "1"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(j\), \(1\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["k", "1"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(k\), \(1\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["l", "1"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(l\), \(1\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["i", "2"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(i\), \(2\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["j", "2"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(j\), \(2\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["k", "2"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(k\), \(2\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["l", "2"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(l\), \(2\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["i", "3"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(i\), \(3\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["j", "3"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(j\), \(3\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["k", "3"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(k\), \(3\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["l", "3"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(l\), \(3\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["i", "4"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(i\), \(4\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["j", "4"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(j\), \(4\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["k", "4"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(k\), \(4\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{
      SubscriptBox["l", "4"], "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<\!\(\*SubscriptBox[\(l\), \(4\)]\)\>\"", ",", "occ"}], 
       "]"}]}], ";"}], "\[IndentingNewLine]", "\n", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"a", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<a\>\"", ",", "virt"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"b", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<b\>\"", ",", "virt"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"c", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<c\>\"", ",", "virt"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"d", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<d\>\"", ",", "virt"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"e", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<e\>\"", ",", "virt"}], "]"}]}], ";"}], "\n", 
    RowBox[{
     RowBox[{"f", "=", 
      RowBox[{"createParticleIndex", "[", 
       RowBox[{"\"\<f\>\"", ",", "virt"}], "]"}]}], ";"}]}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["a", "1"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(a\), \(1\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["b", "1"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(b\), \(1\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["c", "1"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(c\), \(1\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["d", "1"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(d\), \(1\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["a", "2"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(a\), \(2\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["b", "2"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(b\), \(2\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["c", "2"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(c\), \(2\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["d", "2"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(d\), \(2\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["a", "3"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(a\), \(3\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["b", "3"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(b\), \(3\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["c", "3"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(c\), \(3\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["d", "3"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(d\), \(3\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["a", "4"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(a\), \(4\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["b", "4"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(b\), \(4\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["c", "4"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(c\), \(4\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["d", "4"], "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\!\(\*SubscriptBox[\(d\), \(4\)]\)\>\"", ",", "virt"}], 
      "]"}]}], ";"}], "\n", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"\[Kappa]", "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\[Kappa]\>\"", ",", "allany"}], "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{"\[Lambda]", "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\[Lambda]\>\"", ",", "allany"}], "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{"\[Mu]", "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\[Mu]\>\"", ",", "allany"}], "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{"\[Nu]", "=", 
     RowBox[{"createParticleIndex", "[", 
      RowBox[{"\"\<\[Nu]\>\"", ",", "allany"}], "]"}]}], ";"}], "\n", 
   "\[IndentingNewLine]", 
   StyleBox[
    RowBox[{"(*", " ", "Hamiltonian", " ", "*)"}], "SmallText"], 
   StyleBox["\[IndentingNewLine]", "SmallText"], 
   RowBox[{
    RowBox[{"g2", "=", 
     RowBox[{"createSQM", "[", 
      RowBox[{"\"\<\!\(\*OverscriptBox[\(g\), \(_\)]\)\>\"", ",", 
       RowBox[{"{", 
        RowBox[{"\[Mu]", ",", "\[Nu]"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"\[Kappa]", ",", "\[Lambda]"}], "}"}], ",", "antisymm"}], 
      "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{"ga2", "=", 
     RowBox[{"createSQS", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"\[Mu]", ",", "\[Nu]"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"\[Kappa]", ",", "\[Lambda]"}], "}"}]}], "]"}]}], ";"}], "\n",
    
   RowBox[{
    RowBox[{"H2", "=", 
     RowBox[{
      RowBox[{"1", "/", "4"}], " ", "g2", "*", "ga2"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{"f1", "=", 
     RowBox[{"createSQM", "[", 
      RowBox[{"\"\<F\>\"", ",", 
       RowBox[{"{", "\[Mu]", "}"}], ",", 
       RowBox[{"{", "\[Nu]", "}"}], ",", "antisymm"}], "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{"ga1", "=", 
     RowBox[{"createSQS", "[", 
      RowBox[{
       RowBox[{"{", "\[Mu]", "}"}], ",", 
       RowBox[{"{", "\[Nu]", "}"}]}], "]"}]}], ";"}], "\n", 
   RowBox[{
    RowBox[{"H1", "=", " ", 
     RowBox[{"f1", "*", "ga1"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"H", "=", 
     RowBox[{"H1", "+", "H2"}]}], ";"}], "\[IndentingNewLine]", 
   StyleBox["\n", "SmallText"], 
   StyleBox[
    RowBox[{"(*", "\[IndentingNewLine]", 
     RowBox[{"Cluster", " ", "operators"}], "\[IndentingNewLine]", "*)"}], 
    "SmallText"], "\n", 
   RowBox[{
    RowBox[{
     SubscriptBox["T1", "1"], "=", 
     RowBox[{
      RowBox[{"createSQM", "[", 
       RowBox[{"\"\<t\>\"", ",", 
        RowBox[{"{", 
         SubscriptBox["a", "1"], "}"}], ",", 
        RowBox[{"{", 
         SubscriptBox["i", "1"], "}"}], ",", "antisymm"}], "]"}], "*", 
      RowBox[{"createSQS", "[", 
       RowBox[{
        RowBox[{"{", 
         SubscriptBox["a", "1"], "}"}], ",", 
        RowBox[{"{", 
         SubscriptBox["i", "1"], "}"}]}], "]"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T1", "2"], "=", 
     RowBox[{
      RowBox[{"createSQM", "[", 
       RowBox[{"\"\<t\>\"", ",", 
        RowBox[{"{", 
         SubscriptBox["a", "2"], "}"}], ",", 
        RowBox[{"{", 
         SubscriptBox["i", "2"], "}"}], ",", "antisymm"}], "]"}], "*", 
      RowBox[{"createSQS", "[", 
       RowBox[{
        RowBox[{"{", 
         SubscriptBox["a", "2"], "}"}], ",", 
        RowBox[{"{", 
         SubscriptBox["i", "2"], "}"}]}], "]"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T1", "3"], "=", 
     RowBox[{
      RowBox[{"createSQM", "[", 
       RowBox[{"\"\<t\>\"", ",", 
        RowBox[{"{", 
         SubscriptBox["a", "3"], "}"}], ",", 
        RowBox[{"{", 
         SubscriptBox["i", "3"], "}"}], ",", "antisymm"}], "]"}], "*", 
      RowBox[{"createSQS", "[", 
       RowBox[{
        RowBox[{"{", 
         SubscriptBox["a", "3"], "}"}], ",", 
        RowBox[{"{", 
         SubscriptBox["i", "3"], "}"}]}], "]"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T1", "4"], "=", 
     RowBox[{
      RowBox[{"createSQM", "[", 
       RowBox[{"\"\<t\>\"", ",", 
        RowBox[{"{", 
         SubscriptBox["a", "4"], "}"}], ",", 
        RowBox[{"{", 
         SubscriptBox["i", "4"], "}"}], ",", "antisymm"}], "]"}], "*", 
      RowBox[{"createSQS", "[", 
       RowBox[{
        RowBox[{"{", 
         SubscriptBox["a", "4"], "}"}], ",", 
        RowBox[{"{", 
         SubscriptBox["i", "4"], "}"}]}], "]"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T2", "1"], "=", 
     RowBox[{
      RowBox[{"1", "/", "4"}], "*", 
      RowBox[{"createSQM", "[", 
       RowBox[{"\"\<t\>\"", ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["a", "1"], ",", 
          SubscriptBox["b", "1"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["i", "1"], ",", 
          SubscriptBox["j", "1"]}], "}"}], ",", "antisymm"}], "]"}], "*", 
      RowBox[{"createSQS", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["a", "1"], ",", 
          SubscriptBox["b", "1"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["i", "1"], ",", 
          SubscriptBox["j", "1"]}], "}"}]}], "]"}]}]}], ";"}], 
   StyleBox["\[IndentingNewLine]", "SmallText"], 
   RowBox[{
    RowBox[{
     SubscriptBox["T2", "2"], "=", 
     RowBox[{
      RowBox[{"1", "/", "4"}], "*", 
      RowBox[{"createSQM", "[", 
       RowBox[{"\"\<t\>\"", ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["a", "2"], ",", 
          SubscriptBox["b", "2"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["i", "2"], ",", 
          SubscriptBox["j", "2"]}], "}"}], ",", "antisymm"}], "]"}], "*", 
      RowBox[{"createSQS", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["a", "2"], ",", 
          SubscriptBox["b", "2"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["i", "2"], ",", 
          SubscriptBox["j", "2"]}], "}"}]}], "]"}]}]}], ";"}], 
   StyleBox["\[IndentingNewLine]", "SmallText"], 
   RowBox[{
    RowBox[{
     SubscriptBox["T2", "3"], "=", 
     RowBox[{
      RowBox[{"1", "/", "4"}], "*", 
      RowBox[{"createSQM", "[", 
       RowBox[{"\"\<t\>\"", ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["a", "3"], ",", 
          SubscriptBox["b", "3"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["i", "3"], ",", 
          SubscriptBox["j", "3"]}], "}"}], ",", "antisymm"}], "]"}], "*", 
      RowBox[{"createSQS", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["a", "3"], ",", 
          SubscriptBox["b", "3"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["i", "3"], ",", 
          SubscriptBox["j", "3"]}], "}"}]}], "]"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T2", "4"], "=", 
     RowBox[{
      RowBox[{"1", "/", "4"}], "*", 
      RowBox[{"createSQM", "[", 
       RowBox[{"\"\<t\>\"", ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["a", "4"], ",", 
          SubscriptBox["b", "4"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["i", "4"], ",", 
          SubscriptBox["j", "4"]}], "}"}], ",", "antisymm"}], "]"}], "*", 
      RowBox[{"createSQS", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["a", "4"], ",", 
          SubscriptBox["b", "4"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          SubscriptBox["i", "4"], ",", 
          SubscriptBox["j", "4"]}], "}"}]}], "]"}]}]}], ";"}], 
   StyleBox["\[IndentingNewLine]", "SmallText"], 
   StyleBox["\[IndentingNewLine]", "SmallText"], 
   StyleBox[
    RowBox[{"(*", " ", 
     RowBox[{"projection", " ", "operators"}], " ", "*)"}], "SmallText"], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"P1", "=", 
     RowBox[{"createSQS", "[", 
      RowBox[{
       RowBox[{"{", "i", "}"}], ",", 
       RowBox[{"{", "a", "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"P2", "=", 
     RowBox[{"createSQS", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"i", ",", "j"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"a", ",", "b"}], "}"}]}], "]"}]}], ";"}], 
   StyleBox["\[IndentingNewLine]", "SmallText"], "\[IndentingNewLine]", 
   StyleBox[
    RowBox[{"(*", " ", 
     RowBox[{
     "The", " ", "function", " ", "processes", " ", "expressions", " ", 
      "after", " ", 
      RowBox[{"Wick", "'"}], "s", " ", "theorem"}], " ", "*)"}], "SmallText"],
    "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"process", "[", 
      RowBox[{"expr_", ",", 
       RowBox[{"extIndices_List:", 
        RowBox[{"{", "}"}]}], ",", 
       RowBox[{"params_List:", "defaultTheoryParams"}]}], "]"}], ":=", 
     "\[IndentingNewLine]", 
     RowBox[{"Module", "[", 
      RowBox[{
       RowBox[{"{", "result", "}"}], ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"result", "=", "expr"}], ";", "\[IndentingNewLine]", 
        RowBox[{"If", "[", 
         RowBox[{
          RowBox[{"useBrillouin", "/.", "params"}], ",", 
          RowBox[{"result", "=", 
           RowBox[{"brillouin", "[", "result", "]"}]}]}], "]"}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"If", "[", 
         RowBox[{
          RowBox[{"keepDisconnected", "/.", "params"}], ",", ",", 
          RowBox[{"result", "=", 
           RowBox[{"removeDisconnectedTerms", "[", 
            RowBox[{"result", ",", "extIndices"}], "]"}]}]}], "]"}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"If", "[", 
         RowBox[{
          RowBox[{"doSimplify", "/.", "params"}], ",", 
          RowBox[{"result", "=", 
           RowBox[{"Simplify", "[", "result", "]"}]}]}], "]"}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"Return", "[", "result", "]"}], ";"}]}], 
      "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", 
   StyleBox["\[IndentingNewLine]", "SmallText"], 
   StyleBox["\[IndentingNewLine]", "SmallText"], 
   StyleBox[
    RowBox[{"(*", " ", 
     RowBox[{"Print", " ", "definitions"}], " ", "*)"}], "SmallText"], 
   StyleBox["\[IndentingNewLine]", "SmallText"], 
   RowBox[{
    RowBox[{
     StyleBox["Print", "Commentary"], 
     StyleBox["[", "Commentary"], 
     RowBox[{
      StyleBox["\"\<Hamiltonian: \>\"", "Commentary"], 
      StyleBox[",", "Commentary"], 
      RowBox[{"H", "//", "TraditionalForm"}]}], "]"}], ";"}]}]}]], "Input"],

Cell[BoxData[
 SuperscriptBox["Null", "28"]], "Output",
 CellChangeTimes->{3.405108163547063*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Hamiltonian: \"\>", "\[InvisibleSpace]", 
   TagBox[
    FormBox[
     RowBox[{
      RowBox[{
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"F\"\>", "\<\"\[Mu]\"\>", "\<\"\[Nu]\"\>"],
         Subsuperscript["F", "\[Mu]", "\[Nu]"],
         Editable->False],
        TraditionalForm], " ", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"\[ATilde]\"\>", "\<\"\[Nu]\"\>", "\<\"\[Mu]\"\
\>"],
         Subsuperscript["\[ATilde]", "\[Nu]", "\[Mu]"],
         Editable->False],
        TraditionalForm]}], "+", 
      RowBox[{
       FractionBox["1", "4"], " ", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\"\
\>", "\<\"\[Mu]\[Nu]\"\>", "\<\"\[Kappa]\[Lambda]\"\>"],
         Subsuperscript[
         "\!\(\*OverscriptBox[\(g\), \(_\)]\)", "\[Mu]\[Nu]", 
          "\[Kappa]\[Lambda]"],
         Editable->False],
        TraditionalForm], " ", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"\[ATilde]\"\>", "\<\"\[Kappa]\[Lambda]\"\>", \
"\<\"\[Mu]\[Nu]\"\>"],
         Subsuperscript["\[ATilde]", "\[Kappa]\[Lambda]", "\[Mu]\[Nu]"],
         Editable->False],
        TraditionalForm]}]}],
     TraditionalForm],
    TraditionalForm,
    Editable->True]}],
  SequenceForm["Hamiltonian: ", 
   TraditionalForm[$CellContext`SQM[
       $CellContext`OHead["F", 
        $CellContext`indexSymm[-1]], 
       $CellContext`particleIndex["\[Mu]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`bra]], 
       $CellContext`particleIndex["\[Nu]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`ket]]] $CellContext`SQS[
       $CellContext`particleIndex["\[Mu]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`cre]], 
       $CellContext`particleIndex["\[Nu]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`ann]]] + 
    Rational[1, 4] $CellContext`SQM[
       $CellContext`OHead["\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
        $CellContext`indexSymm[-1]], 
       $CellContext`particleIndex["\[Mu]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`bra]], 
       $CellContext`particleIndex["\[Nu]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`bra]], 
       $CellContext`particleIndex["\[Kappa]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`ket]], 
       $CellContext`particleIndex["\[Lambda]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`ket]]] $CellContext`SQS[
       $CellContext`particleIndex["\[Mu]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`cre]], 
       $CellContext`particleIndex["\[Nu]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`cre]], 
       $CellContext`particleIndex["\[Lambda]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`ann]], 
       $CellContext`particleIndex["\[Kappa]", 
        $CellContext`particleSpace[$CellContext`occupied, \
$CellContext`othervirtual, $CellContext`virtual], 
        $CellContext`indexType[$CellContext`ann]]]]],
  Editable->False]], "Print",
 CellChangeTimes->{3.405108163583345*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Choose CC Ansatz", "Subsubtitle"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", "\[IndentingNewLine]", 
    RowBox[{"CCSD", " ", "Cluster", " ", "Operators"}], "\[IndentingNewLine]",
     "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{
     SubscriptBox["T", "1"], " ", "=", " ", 
     RowBox[{
      SubscriptBox["T1", "1"], "+", 
      SubscriptBox["T2", "1"]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T", "2"], " ", "=", " ", 
     RowBox[{
      SubscriptBox["T1", "2"], "+", 
      SubscriptBox["T2", "2"]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T", "3"], " ", "=", " ", 
     RowBox[{
      SubscriptBox["T1", "3"], "+", 
      SubscriptBox["T2", "3"]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T", "4"], " ", "=", " ", 
     RowBox[{
      SubscriptBox["T1", "4"], "+", 
      SubscriptBox["T2", "4"]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     StyleBox["Print", "Commentary"], 
     StyleBox["[", "Commentary"], 
     RowBox[{
      StyleBox["\"\<Cluster operator: \>\"", "Commentary"], 
      StyleBox[",", "Commentary"], 
      RowBox[{
       SubscriptBox["T", "1"], "//", "TraditionalForm"}]}], "]"}], ";"}], 
   "\[IndentingNewLine]"}]}]], "Input"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Cluster operator: \"\>", "\[InvisibleSpace]", 
   TagBox[
    FormBox[
     RowBox[{
      RowBox[{
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
         Subsuperscript[
         "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
          "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
         Editable->False],
        TraditionalForm], " ", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"\[ATilde]\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
         Subsuperscript[
         "\[ATilde]", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
          "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
         Editable->False],
        TraditionalForm]}], "+", 
      RowBox[{
       FractionBox["1", "4"], " ", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(b\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(j\\), \
\\(1\\)]\\)\"\>"],
         Subsuperscript[
         "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(b\), \
\(1\)]\)", 
          "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(j\), \(1\)]\
\)"],
         Editable->False],
        TraditionalForm], " ", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"\[ATilde]\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(j\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(b\\), \\(1\\)]\\)\"\>"],
         Subsuperscript[
         "\[ATilde]", 
          "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(j\), \(1\)]\
\)", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(b\), \(1\)]\)"],
         Editable->False],
        TraditionalForm]}]}],
     TraditionalForm],
    TraditionalForm,
    Editable->True]}],
  SequenceForm["Cluster operator: ", 
   TraditionalForm[$CellContext`SQM[
       $CellContext`OHead["t", 
        $CellContext`indexSymm[-1]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`virtual], 
        $CellContext`indexType[$CellContext`bra]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`occupied], 
        $CellContext`indexType[$CellContext`ket]]] $CellContext`SQS[
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`virtual], 
        $CellContext`indexType[$CellContext`cre]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`occupied], 
        $CellContext`indexType[$CellContext`ann]]] + 
    Rational[1, 4] $CellContext`SQM[
       $CellContext`OHead["t", 
        $CellContext`indexSymm[-1]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`virtual], 
        $CellContext`indexType[$CellContext`bra]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(b\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`virtual], 
        $CellContext`indexType[$CellContext`bra]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`occupied], 
        $CellContext`indexType[$CellContext`ket]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(j\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`occupied], 
        $CellContext`indexType[$CellContext`ket]]] $CellContext`SQS[
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`virtual], 
        $CellContext`indexType[$CellContext`cre]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(b\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`virtual], 
        $CellContext`indexType[$CellContext`cre]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(j\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`occupied], 
        $CellContext`indexType[$CellContext`ann]], 
       $CellContext`particleIndex["\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
        $CellContext`particleSpace[$CellContext`occupied], 
        $CellContext`indexType[$CellContext`ann]]]]],
  Editable->False]], "Print",
 CellChangeTimes->{3.405108172238615*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", "\[IndentingNewLine]", 
    RowBox[{"CCD", " ", "Cluster", " ", "Operators"}], "\[IndentingNewLine]", 
    "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{
     SubscriptBox["T", "1"], " ", "=", " ", 
     SubscriptBox["T2", "1"]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T", "2"], " ", "=", " ", 
     SubscriptBox["T2", "2"]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T", "3"], " ", "=", " ", 
     SubscriptBox["T2", "3"]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     SubscriptBox["T", "4"], " ", "=", " ", 
     SubscriptBox["T2", "4"]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     StyleBox["Print", "Commentary"], 
     StyleBox["[", "Commentary"], 
     RowBox[{
      StyleBox["\"\<Cluster operator: \>\"", "Commentary"], 
      StyleBox[",", "Commentary"], 
      RowBox[{
       SubscriptBox["T", "1"], "//", "TraditionalForm"}]}], "]"}], ";"}], 
   "\[IndentingNewLine]"}]}]], "Input"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Cluster operator: \"\>", "\[InvisibleSpace]", 
   TagBox[
    FormBox[
     RowBox[{
      RowBox[{
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(a\\_1\\)\"\>", \
"\<\"\\!\\(i\\_1\\)\"\>"],
         Subsuperscript["t", "\!\(a\_1\)", "\!\(i\_1\)"],
         Editable->False],
        TraditionalForm], " ", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"\[ATilde]\"\>", "\<\"\\!\\(i\\_1\\)\"\>", "\<\
\"\\!\\(a\\_1\\)\"\>"],
         Subsuperscript["\[ATilde]", "\!\(i\_1\)", "\!\(a\_1\)"],
         Editable->False],
        TraditionalForm]}], "+", 
      RowBox[{
       FractionBox["1", "4"], " ", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"t\"\>", \
"\<\"\\!\\(a\\_1\\)\\!\\(b\\_1\\)\"\>", \
"\<\"\\!\\(i\\_1\\)\\!\\(j\\_1\\)\"\>"],
         Subsuperscript["t", "\!\(a\_1\)\!\(b\_1\)", "\!\(i\_1\)\!\(j\_1\)"],
         Editable->False],
        TraditionalForm], " ", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"\[ATilde]\"\>", \
"\<\"\\!\\(i\\_1\\)\\!\\(j\\_1\\)\"\>", \
"\<\"\\!\\(a\\_1\\)\\!\\(b\\_1\\)\"\>"],
         Subsuperscript[
         "\[ATilde]", "\!\(i\_1\)\!\(j\_1\)", "\!\(a\_1\)\!\(b\_1\)"],
         Editable->False],
        TraditionalForm]}]}],
     TraditionalForm],
    TraditionalForm,
    Editable->True]}],
  SequenceForm["Cluster operator: ", 
   TraditionalForm[SQM[
       OHead["t", 
        indexSymm[-1]], 
       particleIndex["\!\(a\_1\)", 
        particleSpace[virtual], 
        indexType[bra]], 
       particleIndex["\!\(i\_1\)", 
        particleSpace[occupied], 
        indexType[ket]]] SQS[
       particleIndex["\!\(a\_1\)", 
        particleSpace[virtual], 
        indexType[cre]], 
       particleIndex["\!\(i\_1\)", 
        particleSpace[occupied], 
        indexType[ann]]] + Rational[1, 4] SQM[
       OHead["t", 
        indexSymm[-1]], 
       particleIndex["\!\(a\_1\)", 
        particleSpace[virtual], 
        indexType[bra]], 
       particleIndex["\!\(b\_1\)", 
        particleSpace[virtual], 
        indexType[bra]], 
       particleIndex["\!\(i\_1\)", 
        particleSpace[occupied], 
        indexType[ket]], 
       particleIndex["\!\(j\_1\)", 
        particleSpace[occupied], 
        indexType[ket]]] SQS[
       particleIndex["\!\(a\_1\)", 
        particleSpace[virtual], 
        indexType[cre]], 
       particleIndex["\!\(b\_1\)", 
        particleSpace[virtual], 
        indexType[cre]], 
       particleIndex["\!\(j\_1\)", 
        particleSpace[occupied], 
        indexType[ann]], 
       particleIndex["\!\(i\_1\)", 
        particleSpace[occupied], 
        indexType[ann]]]]],
  Editable->False]], "Print"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Set Theory Parameters", "Subsubtitle"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"defaultTheoryParams", "=", "\[IndentingNewLine]", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"useBrillouin", "\[Rule]", "False"}], ",", "\[IndentingNewLine]",
      
     RowBox[{"keepDisconnected", "\[Rule]", "False"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"doSimplify", "\[Rule]", "True"}]}], "\[IndentingNewLine]", 
    "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"theoryParams", "=", "defaultTheoryParams"}], 
  ";"}], "\[IndentingNewLine]"}], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Deriving Full CC-R12 Equations", "Subtitle"],

Cell["Energy equations", "Subsubtitle"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{"H", "**", "T"}], "->", "0"}], " ", "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"H", "**", 
        SubscriptBox["T", "1"]}], ",", 
       RowBox[{"{", "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", 
       RowBox[{"{", "}"}], ",", "theoryParams"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\
\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
       "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\
\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
       "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FractionBox["1", "4"], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(j\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(b\\), \
\\(1\\)]\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(j\), \(1\)]\)",
        "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(b\), \
\(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\
\\)]\\)\\!\\(\\*SubscriptBox[\\(b\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(j\\), \
\\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(b\), \
\(1\)]\)", 
       "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(j\), \
\(1\)]\)"],
      Editable->False],
     TraditionalForm]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.405108177905437*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
      RowBox[{"1", "/", "2"}], " ", 
      RowBox[{"H", "**", "T", "**", "T"}]}], "->", "0"}], " ", "*)"}], 
   "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"H", "**", 
        SubscriptBox["T", "1"], "**", 
        SubscriptBox["T", "2"]}], ",", 
       RowBox[{"{", "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "/=", "2"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", 
       RowBox[{"{", "}"}], ",", "theoryParams"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox["1", "2"], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
     Subsuperscript[
     "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
      "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
     Editable->False],
    TraditionalForm], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
     Subsuperscript[
     "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
      "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
     Editable->False],
    TraditionalForm], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>"],
     Subsuperscript[
     "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
      "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \(2\)]\)", 
      "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\)]\)"],
     
     Editable->False],
    TraditionalForm]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.405108182625222*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["T1 Amplitude Equations", "Subsubtitle"],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{"set", " ", "T1", " ", "external", " ", "indices"}], " ", "*)"}], 
   "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{"T1ExtIndices", "=", 
    RowBox[{"{", 
     RowBox[{"i", ",", "a"}], "}"}]}], ";"}]}]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{"H", "**", "T"}], "->", "T1"}], " ", "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"P1", "**", "H", "**", 
        SubscriptBox["T", "1"]}], ",", "T1ExtIndices"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", "T1ExtIndices", ",", "theoryParams"}], "]"}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"-", 
     FormBox[
      InterpretationBox[
       SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\"\>", "\<\"i\"\>"],
       Subsuperscript["F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", "i"],
       Editable->False],
      TraditionalForm]}], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", "\<\"\\!\\(\\*SubscriptBox[\
\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"F\"\>", "\<\"a\"\>", "\<\"\\!\\(\\*SubscriptBox[\
\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript["F", "a", "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\
\\)]\\)\"\>", "\<\"i\"\>"],
      Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\
\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
       "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
       "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\
\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
       "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
       "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(j\\), \\(1\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(j\), \(1\)]\)",
        "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(j\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
       "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(j\), \
\(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(b\\), \
\\(1\\)]\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
       "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(b\), \
\(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\
\\)]\\)\\!\\(\\*SubscriptBox[\\(b\\), \\(1\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(b\), \
\(1\)]\)", "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.405108190423738*^9, 3.40510819602773*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
      RowBox[{"1", "/", "2"}], " ", 
      RowBox[{"H", "**", "T", "**", "T"}]}], "->", "T1"}], " ", "*)"}], 
   "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"P1", "**", "H", "**", 
        SubscriptBox["T", "1"], "**", 
        SubscriptBox["T", "2"]}], ",", "T1ExtIndices"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", "T1ExtIndices", ",", "theoryParams"}], "]"}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "/=", "2"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox["1", "2"], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", "2"}], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{"2", " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
            "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
            "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
            
            "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
           Editable->False],
          TraditionalForm]}], "-", 
        RowBox[{
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
            "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
            "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", \
"\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \
\\(2\\)]\\)\"\>"],
           Subsuperscript[
           "t", "a\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
            "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)"],
           Editable->False],
          TraditionalForm]}]}], ")"}], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\
\)]\)", "i\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm]}]}], ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.405108204649393*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
      RowBox[{"1", "/", "6"}], " ", 
      RowBox[{"H", "**", "T1", "**", "T1", "**", "T1"}]}], "->", "T1"}], " ", 
    "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"P1", "**", "H", "**", 
        SubscriptBox["T1", "1"], "**", 
        SubscriptBox["T1", "2"], "**", 
        SubscriptBox["T1", "3"]}], ",", "T1ExtIndices"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", "T1ExtIndices", ",", "theoryParams"}], "]"}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "/=", "6"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", "\<\"\\!\\(\\*SubscriptBox[\
\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\"\>"],
     Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
     Editable->False],
    TraditionalForm], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
     Subsuperscript[
     "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
      "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
     Editable->False],
    TraditionalForm], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>"],
     Subsuperscript[
     "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
      "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \(2\)]\)", 
      "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\)]\)"],
     
     Editable->False],
    TraditionalForm]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.405108208932691*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["T2 Amplitude Equations", "Subsubtitle"],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{"set", " ", "T2", " ", "external", " ", "indices"}], " ", "*)"}], 
   "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{"T2ExtIndices", "=", 
    RowBox[{"{", 
     RowBox[{"i", ",", "j", ",", "a", ",", "b"}], "}"}]}], ";"}]}]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{"H", "**", "T"}], "->", "T2"}], " ", "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"P2", "**", "H", "**", 
        SubscriptBox["T", "1"]}], ",", "T2ExtIndices"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", "T2ExtIndices", ",", "theoryParams"}], "]"}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\
\\)]\\)\"\>", "\<\"j\"\>"],
      Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "j"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"ab\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\
\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", "ab", 
       "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "-", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\
\\)]\\)\"\>", "\<\"i\"\>"],
      Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"ab\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\
\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", "ab", 
       "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "-", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", "\<\"\\!\\(\\*SubscriptBox[\
\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"ij\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", "ij"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", "\<\"\\!\\(\\*SubscriptBox[\
\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"ij\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", "ij"],
      Editable->False],
     TraditionalForm]}], "-", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\
\\)]\\)\"\>", "\<\"j\"\>"],
      Subsuperscript["F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", "j"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript["t", "ab", "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\
\\)]\\)\"\>", "\<\"i\"\>"],
      Subsuperscript["F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", "i"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript["t", "ab", "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(j\\), \\(1\\)]\\)\"\>", "\<\"ij\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(j\), \(1\)]\)",
        "ij"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(j\\), \
\\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "ab", 
       "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(j\), \
\(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"F\"\>", "\<\"b\"\>", "\<\"\\!\\(\\*SubscriptBox[\
\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript["F", "b", "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
      Subsuperscript["t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
       "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
       "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "-", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
       "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
       "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "-", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"F\"\>", "\<\"a\"\>", "\<\"\\!\\(\\*SubscriptBox[\
\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript["F", "a", "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
      Subsuperscript["t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
      Editable->False],
     TraditionalForm]}], "-", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
       "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
       "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
       "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
       "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
       "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
      Editable->False],
     TraditionalForm]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"ab\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(b\\), \\(1\\)]\\)\"\>"],
      Subsuperscript[
      "\!\(\*OverscriptBox[\(g\), \(_\)]\)", "ab", 
       "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(b\), \
\(1\)]\)"],
      Editable->False],
     TraditionalForm], " ", 
    FormBox[
     InterpretationBox[
      SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\
\\)]\\)\\!\\(\\*SubscriptBox[\\(b\\), \\(1\\)]\\)\"\>", "\<\"ij\"\>"],
      Subsuperscript[
      "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(b\), \
\(1\)]\)", "ij"],
      Editable->False],
     TraditionalForm]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.405108225466776*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
      RowBox[{"1", "/", "2"}], " ", 
      RowBox[{"H", "**", "T", "**", "T"}]}], "->", "T2"}], " ", "*)"}], 
   "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"P2", "**", "H", "**", 
        SubscriptBox["T", "1"], "**", 
        SubscriptBox["T", "2"]}], ",", "T2ExtIndices"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", "T2ExtIndices", ",", "theoryParams"}], "]"}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "/=", "2"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox["1", "2"], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       FormBox[
        InterpretationBox[
         SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
         Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
         Editable->False],
        TraditionalForm]}], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "ab", "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "ab", "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "j"],
        Editable->False],
       TraditionalForm], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"-", 
          FormBox[
           InterpretationBox[
            
            SubsuperscriptBox["\<\"t\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", "\<\"i\"\>"],
            Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "i"],
            Editable->False],
           TraditionalForm]}], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"ab\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", "ab", 
            "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
           Editable->False],
          TraditionalForm]}], "-", 
        RowBox[{"2", " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
           Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
            "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
            "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
           Editable->False],
          TraditionalForm]}], "+", 
        RowBox[{"2", " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
           Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
            "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
            "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
           Editable->False],
          TraditionalForm]}], "-", 
        RowBox[{"2", " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
            "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
           Subsuperscript["t", "ab", "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
           Editable->False],
          TraditionalForm]}], "+", 
        RowBox[{
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
            "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \
\\(2\\)]\\)\"\>"],
           Subsuperscript[
           "t", "ab", 
            "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)"],
           Editable->False],
          TraditionalForm]}]}], ")"}]}], "+", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
        Editable->False],
       TraditionalForm], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"j\"\>"],
           Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "j"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"ab\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", "ab", 
            "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
           Editable->False],
          TraditionalForm]}], "+", 
        RowBox[{"2", " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
           Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
            "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
            "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
           Editable->False],
          TraditionalForm]}], "-", 
        RowBox[{"2", " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
           Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
            "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
            "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
           Editable->False],
          TraditionalForm]}], "+", 
        RowBox[{"2", " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
            "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
           Subsuperscript["t", "ab", "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
           Editable->False],
          TraditionalForm]}], "-", 
        RowBox[{
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
            "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \
\\(2\\)]\\)\"\>"],
           Subsuperscript[
           "t", "ab", 
            "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)"],
           Editable->False],
          TraditionalForm]}]}], ")"}]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript["t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript["t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"j\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "j"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"i\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "i"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"F\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "F", "\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript["t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript["t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript["t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"j\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "j"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"i\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "i"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "b\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "i\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "b\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "j\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript["t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "b\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\
\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\
\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "ab", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\
\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "ab", "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\
\)]\)", "i\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "ab", "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\
\)]\)", "j\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm]}]}], ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.405108350499494*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
      RowBox[{"1", "/", "6"}], " ", 
      RowBox[{"H", "**", "T1", "**", "T1", "**", "T1"}]}], "->", "T2"}], " ", 
    "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"P2", "**", "H", "**", 
        SubscriptBox["T1", "1"], "**", 
        SubscriptBox["T1", "2"], "**", 
        SubscriptBox["T1", "3"]}], ",", "T2ExtIndices"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", "T2ExtIndices", ",", "theoryParams"}], "]"}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "/=", "6"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input",
 CellChangeTimes->{{3.4051084289612503`*^9, 3.405108438396803*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox["1", "6"], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"6", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
           Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\"\>"],
           Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "j"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\
\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
           Subsuperscript[
           "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
            "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "i\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
           Editable->False],
          TraditionalForm]}], "+", 
        RowBox[{
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\"\>"],
           Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
           Editable->False],
          TraditionalForm], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            FormBox[
             InterpretationBox[
              
              SubsuperscriptBox["\<\"t\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", "\<\"j\"\>"],
              Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "j"],
              Editable->False],
             TraditionalForm], " ", 
            FormBox[
             InterpretationBox[
              
              SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\
\\)\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
              Subsuperscript[
              "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
               "b\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
               "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
              Editable->False],
             TraditionalForm]}], "-", 
           RowBox[{
            FormBox[
             InterpretationBox[
              
              SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
              Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
              Editable->False],
             TraditionalForm], " ", 
            FormBox[
             InterpretationBox[
              
              SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\
\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\"\>"],
              Subsuperscript[
              "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
               "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)", "j\!\(\*SubscriptBox[\(a\), \(1\)]\)"],
              Editable->False],
             TraditionalForm]}]}], ")"}]}]}], ")"}]}], "-", 
     RowBox[{"6", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"j\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "j"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \
\\(_\\)]\\)\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(a\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>"],
        Subsuperscript[
        "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
         "a\!\(\*SubscriptBox[\(i\), \(1\)]\)", 
         "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \
\(2\)]\)"],
        Editable->False],
       TraditionalForm]}]}], ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.40510853684369*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
      RowBox[{"1", "/", "2"}], " ", 
      RowBox[{"H", "**", "T2", "**", "T1", "**", "T1"}]}], "->", "T2"}], " ", 
    "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"P2", "**", "H", "**", 
        SubscriptBox["T2", "1"], "**", 
        SubscriptBox["T1", "2"], "**", 
        SubscriptBox["T1", "3"]}], ",", "T2ExtIndices"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", "T2ExtIndices", ",", "theoryParams"}], "]"}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "/=", "2"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input",
 CellChangeTimes->{{3.4051084289612503`*^9, 3.405108452347505*^9}, {
  3.405108530076866*^9, 3.4051085302883167`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox["1", "2"], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>"],
     Subsuperscript[
     "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
      "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \(2\)]\)", 
      "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\)]\)"],
     
     Editable->False],
    TraditionalForm], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", "2"}], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "j"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "ab", "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
        Editable->False],
       TraditionalForm], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"2", " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
           Subsuperscript[
           "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
            "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
           Subsuperscript["t", "ab", "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
           Editable->False],
          TraditionalForm]}], "+", 
        RowBox[{
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"j\"\>"],
           Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "j"],
           Editable->False],
          TraditionalForm], " ", 
         FormBox[
          InterpretationBox[
           
           SubsuperscriptBox["\<\"t\"\>", "\<\"ab\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \
\\(2\\)]\\)\"\>"],
           Subsuperscript[
           "t", "ab", 
            "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \
\(2\)]\)"],
           Editable->False],
          TraditionalForm]}]}], ")"}]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript["t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"j\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "j"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"i\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "i"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "a\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", 
         "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript["t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"j\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "j"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "i\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "-", 
     RowBox[{"2", " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"i\"\>"],
        Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "i"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"j\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript[
        "t", "b\!\(\*SubscriptBox[\(a\), \(1\)]\)", 
         "j\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm]}], "+", 
     RowBox[{
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
        Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
        Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
        Editable->False],
       TraditionalForm], " ", 
      FormBox[
       InterpretationBox[
        SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>", "\<\"ij\"\>"],
        Subsuperscript[
        "t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\
\)]\)", "ij"],
        Editable->False],
       TraditionalForm]}]}], ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.405108591555091*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
      RowBox[{"1", "/", "24"}], " ", 
      RowBox[{"H", "**", "T1", "**", "T1", "**", "T1", "**", "T1"}]}], "->", 
     "T2"}], " ", "*)"}], "SmallText"], 
  StyleBox["\[IndentingNewLine]", "SmallText"], 
  RowBox[{
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"wick", "[", 
      RowBox[{
       RowBox[{"P2", "**", "H", "**", 
        SubscriptBox["T1", "1"], "**", 
        SubscriptBox["T1", "2"], "**", 
        SubscriptBox["T1", "3"], "**", 
        SubscriptBox["T1", "4"]}], ",", "T2ExtIndices"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "=", 
     RowBox[{"process", "[", 
      RowBox[{"tmp", ",", "T2ExtIndices", ",", "theoryParams"}], "]"}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tmp", "/=", "24"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"tmp", "//", "TraditionalForm"}]}]}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"t\"\>", "\<\"a\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\"\>"],
     Subsuperscript["t", "a", "\!\(\*SubscriptBox[\(i\), \(1\)]\)"],
     Editable->False],
    TraditionalForm], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"t\"\>", "\<\"b\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(2\\)]\\)\"\>"],
     Subsuperscript["t", "b", "\!\(\*SubscriptBox[\(i\), \(2\)]\)"],
     Editable->False],
    TraditionalForm], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\"\>", "\<\"i\"\>"],
     Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(1\)]\)", "i"],
     Editable->False],
    TraditionalForm], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"t\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(2\\)]\\)\"\>", "\<\"j\"\>"],
     Subsuperscript["t", "\!\(\*SubscriptBox[\(a\), \(2\)]\)", "j"],
     Editable->False],
    TraditionalForm], " ", 
   FormBox[
    InterpretationBox[
     SubsuperscriptBox["\<\"\\!\\(\\*OverscriptBox[\\(g\\), \\(_\\)]\\)\"\>", \
"\<\"\\!\\(\\*SubscriptBox[\\(i\\), \\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(i\\), \
\\(2\\)]\\)\"\>", "\<\"\\!\\(\\*SubscriptBox[\\(a\\), \
\\(1\\)]\\)\\!\\(\\*SubscriptBox[\\(a\\), \\(2\\)]\\)\"\>"],
     Subsuperscript[
     "\!\(\*OverscriptBox[\(g\), \(_\)]\)", 
      "\!\(\*SubscriptBox[\(i\), \(1\)]\)\!\(\*SubscriptBox[\(i\), \(2\)]\)", 
      "\!\(\*SubscriptBox[\(a\), \(1\)]\)\!\(\*SubscriptBox[\(a\), \(2\)]\)"],
     
     Editable->False],
    TraditionalForm]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.4051084083669147`*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1114, 757},
WindowMargins->{{-1182, Automatic}, {Automatic, -79}},
FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (April 20, 2007)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[590, 23, 47, 0, 76, "Title"],
Cell[640, 25, 25, 0, 46, "Subtitle"],
Cell[668, 27, 34, 0, 26, "Subsubtitle"],
Cell[CellGroupData[{
Cell[727, 31, 19812, 571, 1439, "Input"],
Cell[20542, 604,