Pensieve header: Testing if vertical flip is a symmetry of SolKV.

SetDirectory["C:/drorbn/AcademicPensieve/Projects/WKO4"];
<< FreeLie.m;
<< AwCalculus.m;
Rs[a_,b_]:= Es[⟨a->LS[0], b->LS[LW@a]⟩, CWS[0]];
α=LS[{x,y}, αs]; β=LS[{x,y}, βs];γ=CWS[{x,y}, γs];
(Subscript[V, 0])=Es[⟨x->α, y->β⟩, γ];
κ=CWS[{x}, κs]; Cap=Es[⟨x->LS[0]⟩,κ];
R4Eqn[V_]=V**(Rs[x,z] // dΔ[x,x,y]) ≡ Rs[y,z]**Rs[x,z]**V;UnitarityEqn[V_] = (V**(V//dA) ≡ Es[⟨x->LS[0], y->LS[0]⟩,CWS[0]]);
CapEqn[V_] = ((V**(Cap//dΔ[x,x,y])//dc[x]//dc[y]) ≡ (Cap(Cap//dσ[x,y])//dc[x]//dc[y]));
βs[x]= 1/4; βs[y]=0;
SeriesSolve[{α, β,γ, κ}, ((ℏ^(-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]), κ, (Subscript[V, 1]),(Subscript[V, 2])}

R4Eqn[(Subscript[V, 1])]@{7}

R4Eqn[(Subscript[V, 2])]@{3}

UnitarityEqn[(Subscript[V, 1])]@{7}

CapEqn[(Subscript[V, 1])]@{3}

κ@{10}

κ1=CWS[{x}, κ1s]; Cap1=Es[⟨x->LS[0]⟩,κ1];
SeriesSolve[κ1, (((Subscript[V, 1])**(Cap1//dΔ[x,x,y])//dc[x]//dc[y]) ≡ (Cap1(Cap1//dσ[x,y])//dc[x]//dc[y]))
];

κ1@{8}

((Subscript[V, 1]) ≡(Rs[x,y]**((Subscript[V, 0])//dA//dS)))@{7}

{TimeUsed[], MaxMemoryUsed[]}