(* ::Package:: *)

(************************************************************************)
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SetDirectory["C:/drorbn/AcademicPensieve/Projects/WKO4"];
<< FreeLie.m;
<< AwCalculus.m;
Rs[a_,b_]:= Es[\[LeftAngleBracket]a->LS[0], b->LS[LW@a]\[RightAngleBracket], CWS[0]];
\[Alpha]=LS[{x,y}, \[Alpha]s]; \[Beta]=LS[{x,y}, \[Beta]s];\[Gamma]=CWS[{x,y}, \[Gamma]s];
Subscript[V, 0]=Es[\[LeftAngleBracket]x->\[Alpha], y->\[Beta]\[RightAngleBracket], \[Gamma]];
\[Kappa]=CWS[{x}, \[Kappa]s]; Cap=Es[\[LeftAngleBracket]x->LS[0]\[RightAngleBracket],\[Kappa]];
R4Eqn[V_]=V**(Rs[x,z] // d\[CapitalDelta][x,x,y]) \[Congruent] Rs[y,z]**Rs[x,z]**V;UnitarityEqn[V_] = (V**(V//dA) \[Congruent] Es[\[LeftAngleBracket]x->LS[0], y->LS[0]\[RightAngleBracket],CWS[0]]);
CapEqn[V_] = ((V**(Cap//d\[CapitalDelta][x,x,y])//dc[x]//dc[y]) \[Congruent] (Cap(Cap//d\[Sigma][x,y])//dc[x]//dc[y]));
\[Beta]s[x]= 1/4; \[Beta]s[y]=0;
SeriesSolve[{\[Alpha], \[Beta],\[Gamma], \[Kappa]}, (\[HBar]^-1 R4Eqn[Subscript[V, 0]]) && UnitarityEqn[Subscript[V, 0]] && CapEqn[Subscript[V, 0]]];
Subscript[V, 1] = ((Subscript[V, 0]//dA)**Rs[x,y])//dS;
Subscript[V, 2] = (Subscript[V, 0]//dA)//dS;
{Subscript[V, 0], \[Kappa], Subscript[V, 1],Subscript[V, 2]}



