(* ::Package:: *)

(* ::Title:: *)
(*This file contains the charge conjugation invariant vectors for 4 gluons*)
(**)


(* ::Subsection:: *)
(*The vectors are named and ordered as:*)


CMCNMBq0g4 = {Vector1,Vector8s,Vector8a,Vector27,Vector20,Vector0};
Basis4g=CMCNMBq0g4;


(* ::Text:: *)
(*Here Vector20=(Vector10+Vector10bar)/Sqrt[2]*)


(* ::Subsection:: *)
(*The explicit forms of the vectors are:*)


Subscript[Vector1, {G1_,G3_,G2_,G4_}]:=(Superscript[\[CapitalDelta], {G1, G3}]*
      Superscript[\[CapitalDelta], {G2, G4}])/(-1 + Nc^2);

Subscript[Vector8s, {G1_,G3_,G2_,G4_}]:= Module[{i1},(Nc*Superscript[d, {G1, G3, i1}]*
      Superscript[d, {i1, G2, G4}])/(2*(-4 + Nc^2)*TR)/Sqrt[Nc^2-1]];

Subscript[Vector8a, {G1_,G3_,G2_,G4_}]:= Module[{i1},(Superscript[f, {G1, G3, i1}]*
      Superscript[f, {i1, G2, G4}])/(2*Nc*TR)]/Sqrt[Nc^2-1];

Subscript[Vector27, {G1_,G3_,G2_,G4_}]:=Module[{i1},((Nc*Superscript[d, {G1, G3, i1}]*Superscript[d, 
          {i1, G2, G4}])/(4*(2 + Nc)) - 
       (Superscript[f, {G1, G4, i1}]*Superscript[f, 
          {i1, G3, G2}])/2 - (Superscript[f, {G1, G3, i1}]*
         Superscript[f, {i1, G2, G4}])/4)/(2*TR) + 
     (Superscript[\[CapitalDelta], {G1, G4}]*Superscript[\[CapitalDelta], 
        {G3, G2}])/4 + (Superscript[\[CapitalDelta], {G1, G2}]*
       Superscript[\[CapitalDelta], {G3, G4}])/4 + 
     (Superscript[\[CapitalDelta], {G1, G3}]*Superscript[\[CapitalDelta], 
        {G2, G4}])/(2*(1 + Nc))]/((1/2)Nc Sqrt[-3+2 Nc+Nc^2]);

Subscript[Vector10, {G1_,G3_,G2_,G4_}]:=Module[{i1},-(Superscript[f, {G1, G3,i1}]*Superscript[f, 
         {i1, G2, G4}])/(4*Nc*TR) - 
     (Superscript[o, {G1, G2, G3, G4}] - Superscript[o, {G3, G2, G1, G4}] + 
       TR^2*Superscript[\[CapitalDelta], {G1, G4}]*
        Superscript[\[CapitalDelta], {G3, G2}] - 
       TR^2*Superscript[\[CapitalDelta], {G1, G2}]*
        Superscript[\[CapitalDelta], {G3, G4}])/(4*TR^2)]/((1/2)Sqrt[4-5 Nc^2+Nc^4]);

Subscript[Vector10bar, {G1_,G3_,G2_,G4_}]:=Module[{i1},-(Superscript[f, {G1, G3,i1}]*
        Superscript[f, {i1, G2, G4}])/(4*Nc*TR) - 
     (Superscript[o, {G1, G4, G3, G2}] - Superscript[o, {G3, G4, G1, G2}] + 
       TR^2*Superscript[\[CapitalDelta], {G1, G4}]*
        Superscript[\[CapitalDelta], {G3, G2}] - 
       TR^2*Superscript[\[CapitalDelta], {G1, G2}]*
        Superscript[\[CapitalDelta], {G3, G4}])/(4*TR^2)]/((1/2)Sqrt[4-5 Nc^2+Nc^4]);

Subscript[Vector20, {G1_,G3_,G2_,G4_}]:=(Subscript[Vector10, {G1,G3,G2,G4}]+Subscript[Vector10bar, {G1,G3,G2,G4}])/Sqrt[2];

Subscript[Vector0, {G1_,G3_,G2_,G4_}]:= Module[{i1},(-(Nc*Superscript[d, {G1, G3, i1}]*Superscript[d, 
           {i1, G2, G4}])/(4*(-2 + Nc)) + 
       (Superscript[f, {G1, G4, i1}]*Superscript[f, 
          {i1, G3, G2}])/2 + (Superscript[f, {G1, G3, i1}]*
         Superscript[f, {i1, G2, G4}])/4)/(2*TR) + 
     (Superscript[\[CapitalDelta], {G1, G2}]*Superscript[\[CapitalDelta], 
        {G3, G4}])/4 + (Superscript[\[CapitalDelta], {G1, G4}]*
       Superscript[\[CapitalDelta], {G2, G3}])/4 - 
     (Superscript[\[CapitalDelta], {G1, G3}]*Superscript[\[CapitalDelta], 
        {G2, G4}])/(2*(-1 + Nc))]/((1/2)Nc Sqrt[-3-2Nc+Nc^2]);


(* ::Text:: *)
(*(Private note: Originally created in Check2gProjectorsFromPaperv2.nb, then modified by replacing N with Nc, normalizing projectors as vectors, renaming G2 <-> G3. Checked in CheckMultipletBasisRecursionPaper.nb 140811. 200115 compared with basis constructed from projectors that was used for checking recursion results, and they agree.)*)
