(* ::Package:: *)

(************************************************************************)
(* This file was generated automatically by the Mathematica front end.  *)
(* It contains Initialization cells from a Notebook file, which         *)
(* typically will have the same name as this file except ending in      *)
(* ".nb" instead of ".m".                                               *)
(*                                                                      *)
(* This file is intended to be loaded into the Mathematica kernel using *)
(* the package loading commands Get or Needs.  Doing so is equivalent   *)
(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
(* automatically each time the parent Notebook file is saved in the     *)
(* Mathematica front end.  Any changes you make to this file will be    *)
(* overwritten.                                                         *)
(************************************************************************)



(* ::Input::Initialization:: *)
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];
V=Es[\[LeftAngleBracket]x->\[Alpha], y->\[Beta]\[RightAngleBracket], \[Gamma]];
\[Kappa]=CWS[{x}, \[Kappa]s]; Cap=Es[\[LeftAngleBracket]x->LS[0]\[RightAngleBracket],\[Kappa]];
\[Omega]=CWS[{x}, \[Omega]s]; Wen=Es[\[LeftAngleBracket]x->LS[0]\[RightAngleBracket],\[Omega]];

R4Eqn=V**(Rs[x,z] // d\[CapitalDelta][x,x,y]) \[Congruent] Rs[y,z]**Rs[x,z]**V ;
CapWen=Cap\[Congruent]((Wen**Cap)//dA[x]//dS[x]);
CapEqn=((V**(Cap//d\[CapitalDelta][x,x,y])//dc[x]//dc[y]) \[Congruent] (Cap*(Cap//d\[Sigma][x,y])//dc[x]//dc[y]));
UnitarityEqn=((V//dA[x]//dA[y])**(Wen*(Wen//d\[Sigma][x,y]))**V) \[Congruent] (Wen//d\[CapitalDelta][x,x,y]);

\[Beta]s[x]= 1/2; \[Beta]s[y]=0;
\[Omega]s[x,x,x]=1;
SeriesSolve[{\[Alpha], \[Beta],\[Gamma], \[Kappa],\[Omega]}, (\[HBar]^-1 R4Eqn)\[And]CapWen\[And]CapEqn\[And]UnitarityEqn];
Column@{V@{5}, \[Kappa]@{5},\[Omega]@{5}}



