(* ::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     *)
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(************************************************************************)



SetDirectory["C:\\drorbn\\AcademicPensieve\\2015-12"];
Get["../Projects/WKO4/FreeLie.m"];
Get["../Projects/WKO4/AwCalculus.m"];


l=LW["l"]; r=LW["r"]; x=LW["x"]; y=LW["y"]; z=LW["z"];
A=LS[{l,r}, as];
V = El[
A // LieMorphism[{l->\[LeftAngleBracket]x->LS[y], y->LS[0]\[RightAngleBracket], r->\[LeftAngleBracket]x->LS[0],y->LS[x]\[RightAngleBracket]}, \[LeftAngleBracket]x,y\[RightAngleBracket], tb],
CWS[0]
] // \[CapitalGamma];
V@{4}


Rl[a_,b_]:= El[\[LeftAngleBracket]a->LS[0], b->LS[LW@a]\[RightAngleBracket], CWS[0]];
iRl[a_,b_]:= El[\[LeftAngleBracket]a->LS[0], b->-LS[LW@a]\[RightAngleBracket], CWS[0]];
Rs[a_,b_]:= Es[\[LeftAngleBracket]a->LS[0], b->LS[LW@a]\[RightAngleBracket], CWS[0]];
iRs[a_,b_]:= Es[\[LeftAngleBracket]a->LS[0], b->-LS[LW@a]\[RightAngleBracket], CWS[0]];
\[CapitalTheta]l[x_,y_, s_] := El[\[LeftAngleBracket]x->LS[s LW@y], y->LS[s LW@x]\[RightAngleBracket], CWS[0]];
\[CapitalTheta]s[x_,y_,s_] := \[CapitalTheta]l[x,y,s] // \[CapitalGamma];
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_,Cap_] := (V**(Cap//d\[CapitalDelta][x,x,y])//dc[x]//dc[y]) \[Congruent] (Cap*(Cap//d\[Sigma][x,y])//dc[x]//dc[y]);



