•ππγ

IsoVector[QuantumField[Particle[AxialVector[0], ___], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Scalar[1], ___], ___], ___][_] := 0 ; QuantumField[Particle[Scalar[1], ___], ___][_] := 0 ;

Lagrangian[ChPTPhoton2[4]]

L _ 6^( ) ((< ÷„ '6 χ^† > + < χ '6 ÷„^† >) '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 7^( ) ((< χ^† '6 ÷„ > - < ÷„^† '6 χ >) '6 (< χ^† '6 ÷„ > - < ÷„^† '6 χ >)) + L _ 4^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 1^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 < ÷s _ ν(÷„) '6 ÷s _ ν(÷„)^† >) + L _ 2^( ) (< ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† > '6 < ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† >) + H _ 2^( ) < χ^† '6 χ > + L _ 5^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 (÷„ '6 χ^† + χ '6 ÷„^†) > + L _ 8^( ) (< ÷„ '6 χ^† '6 ÷„ '6 χ^† > + < χ '6 ÷„^† '6 χ '6 ÷„^† >) + L _ 3^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) '6 ÷s _ ν(÷„)^† > + i L _ 9^( ) (< γ^( ) _ (μ ν) '6 Q '6 ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) > + < γ^( ) _ (μ ν) '6 Q '6 ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† >) + 2 H _ 1^( ) < γ^( ) _ (μ ν) '6 Q '6 γ^( ) _ (μ ν) '6 Q > + L _ 10^( ) < γ^( ) _ (μ ν) '6 Q '6 ÷„ '6 γ^( ) _ (μ ν) '6 Q '6 ÷„^† >

llt = CheckF[(WriteString["stdout", "."] ; UNMSplit[#, x, DropOrder -> 2, DiagonalToU -> True]) & /@ Lagrangian[ChPTPhoton2[4]], "llt3mesonPhoton"] ;

............

llt // Length

11

lltt = (WriteString["stdout", "."] ; ArgumentsSupply[#, x, RenormalizationState[0], ExpansionOrder -> 2, DropOrder -> 2, DiagonalToU -> True]) & /@ llt ;

...........

ArgumentsSupply :: argxpr : Warning : The argument x is already in the expression.

ArgumentsSupply :: argxpr : Warning : The argument x is already in the expression.

ArgumentsSupply :: argxpr : Warning : The argument x is already in the expression.

General :: stop : Further output of ArgumentsSupply :: \" argxpr \" will be suppressed during this calculation.

lll = (WriteString["stdout", "."] ; DiscardTerms[#, Retain -> {Particle[Pion , RenormalizationState[0]] -> 2, Particle[Photon , RenormalizationState[0]] -> 1}, Method -> Expand]) & /@ lltt ;

...........

llle = ExpandU[lll, CommutatorReduce -> True] // Simplify

1/(3 (f _ π^(ó  ))^2) (2 e^( ) (6 L _ 4^( ) (3 Overscript[öõ(3), ->] × Overscript[π^( ), ->] · ∂ _ μ(Overscript[π^( ), ->]) - Overscript[öõ(3), ->] × ∂ _ μ(Overscript[π^( ), ->]) · Overscript[π^( ), ->]) γ^( ) _ μ (m _ π^(ó  ))^2 + 3 L _ 5^( ) (3 Overscript[öõ(3), ->] × Overscript[π^( ), ->] · ∂ _ μ(Overscript[π^( ), ->]) - Overscript[öõ(3), ->] × ∂ _ μ(Overscript[π^( ), ->]) · Overscript[π^( ), ->]) γ^( ) _ μ (m _ π^(ó  ))^2 + L _ 9^( ) (3 Overscript[öõ(3), ->] × ∂ _ μ(Overscript[π^( ), ->]) · ∂ _ ν(Overscript[π^( ), ->]) + i ∂ _ μ(Overscript[π^( ), ->]) · ∂ _ ν(Overscript[π^( ), ->])) (∂ _ μ γ^( ) _ ν^ó  - ∂ _ ν γ^( ) _ μ^ó )))

$IsoIndicesCounter = 0 ;

llll = llle // IsoIndicesSupply // Simplify // IndicesCleanup // CommutatorReduce[#, FullReduce -> True] & // Simplify

1/(3 (f _ π^(ó  ))^2) (2 e^( ) (-6 L _ 4^( ) δ _ (3 k3) f _ (k1 k2 k3) γ^( ) _ μ (π^( )^k2 ∂ _ μ π^( ) _ ó ^k1 - 3 π^( )^k1 ∂ _ μ π^( ) _ ó ^k2) (m _ π^(ó  ))^2 - 3 L _ 5^( ) δ _ (3 k3) f _ (k1 k2 k3) γ^( ) _ μ (π^( )^k2 ∂ _ μ π^( ) _ ó ^k1 - 3 π^( )^k1 ∂ _ μ π^( ) _ ó ^k2) (m _ π^(ó  ))^2 + L _ 9^( ) ∂ _ μ π^( ) _ ó ^k1 (i ∂ _ ν π^( ) _ ó ^k1 + 3 δ _ (3 k3) f _ (k1 k2 k3) ∂ _ ν π^( ) _ ó ^k2) (∂ _ μ γ^( ) _ ν^ó  - ∂ _ ν γ^( ) _ μ^ó )))

fields = {QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Photon, RenormalizationState[0]], LorentzIndex[μ3]][p3]}

{π^( )^I _ 1, π^( )^I _ 2, γ^( ) _ μ _ 3}

melsimplified = FeynRule[llll, fields] // Simplify // SUNReduce[#, FullReduce -> True] & // IndicesCleanup // Simplify

-(4 e^( ) (2 (2 L _ 4^( ) + L _ 5^( )) (p _ 1^μ _ 3 - p _ 2^μ _ 3) (m _ π^(ó  ))^2 + L _ 9^( ) (p _ 2^μ _ 3 p _ 1 · p _ 3 - p _ 1^μ _ 3 p _ 2 · p _ 3)) f _ (3 I _ 1 I _ 2)^(2))/(f _ π^(ó  ))^2

Converted by Mathematica  (July 10, 2003)