•ππππγ

ll = ArgumentsSupply[Lagrangian[ChPTPhoton2[2]], x, RenormalizationState[0], ExpansionOrder -> 4, DropOrder -> 4, DiagonalToU -> True] ;

lll = DiscardTerms[ll, Retain -> {Particle[Pion , RenormalizationState[0]] -> 4, Particle[Photon , RenormalizationState[0]] -> 1}, CommutatorReduce -> True] ;

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

$IsoIndicesCounter = 0 ;

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

1/(24 (f _ π^(ó  ))^2) (e^( ) γ^( ) _ μ (3 δ _ (3 k3) f _ (k1 k2 k3) (π^( )^k4)^2 (π^( )^k2 ∂ _ μ π^( ) _ ó ^k1 - π^( )^k1 ∂ _ μ π^( ) _ ó ^k2) - δ _ (3 k5) π^( )^k1 π^( )^k3 (f _ (k1 k2 k6) f _ (k3 k6 k7) f _ (k4 k5 k7) π^( )^k4 ∂ _ μ π^( ) _ ó ^k2 + f _ (k1 k5 k7) f _ (k2 k6 k7) f _ (k3 k4 k6) π^( )^k2 ∂ _ μ π^( ) _ ó ^k4)))

fields = {QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I3]][p3], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I4]][p4], QuantumField[Particle[Photon, RenormalizationState[0]], LorentzIndex[μ5]][p5]}

{π^( )^I _ 1, π^( )^I _ 2, π^( )^I _ 3, π^( )^I _ 4, γ^( ) _ μ _ 5}

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

1/(3 (f _ π^(ó  ))^2) (2 e^( ) (-p _ 3^μ _ 5 δ _ (I _ 2 I _ 4)^(2) f _ (3 I _ 1 I _ 3)^(2) - p _ 4^μ _ 5 δ _ (I _ 2 I _ 3)^(2) f _ (3 I _ 1 I _ 4)^(2) + p _ 1^μ _ 5 (δ _ (I _ 3 I _ 4)^(2) f _ (3 I _ 1 I _ 2)^(2) + δ _ (I _ 2 I _ 4)^(2) f _ (3 I _ 1 I _ 3)^(2) + δ _ (I _ 2 I _ 3)^(2) f _ (3 I _ 1 I _ 4)^(2)) - p _ 3^μ _ 5 δ _ (I _ 1 I _ 4)^(2) f _ (3 I _ 2 I _ 3)^(2) - p _ 4^μ _ 5 δ _ (I _ 1 I _ 3)^(2) f _ (3 I _ 2 I _ 4)^(2) + p _ 2^μ _ 5 (-δ _ (I _ 3 I _ 4)^(2) f _ (3 I _ 1 I _ 2)^(2) + δ _ (I _ 1 I _ 4)^(2) f _ (3 I _ 2 I _ 3)^(2) + δ _ (I _ 1 I _ 3)^(2) f _ (3 I _ 2 I _ 4)^(2)) + p _ 3^μ _ 5 δ _ (I _ 1 I _ 2)^(2) f _ (3 I _ 3 I _ 4)^(2) - p _ 4^μ _ 5 δ _ (I _ 1 I _ 2)^(2) f _ (3 I _ 3 I _ 4)^(2)))

Converted by Mathematica  (July 10, 2003)