•Aϕ

ll = ArgumentsSupply[Lagrangian[ChPT3[2]], x, RenormalizationState[0], ExpansionOrder -> 1, DropOrder -> 1, DiagonalToU -> True] ;

lll = DiscardTerms[ll, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 1, Particle[AxialVector[0] , RenormalizationState[0]] -> 1}, CommutatorReduce -> True, Method -> Coefficient] // Simplify

-1/8 f _ ϕ^(ó  ) (2 < ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] > + 2 < Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] > - i (< Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[V^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] > + < Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[V^( ) _ μ, ->] · Overscript[σ, ->] > - < Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[V^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > - < Overscript[V^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] >))

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

$IsoIndicesCounter = 0 ;

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

1/4 i f _ ϕ^(ó  ) (4 i ∂ _ τ1 ϕ^( ) _ ó ^k1 A^( ) _ τ1^k1 - (d _ (k1 k2 k3)^(3) + i f _ (k1 k2 k3)^(3)) ((ϕ^( )^k3 A^( ) _ ρ1^k1 - ϕ^( )^k1 A^( ) _ ρ1^k3) V^( ) _ ρ1^k2 + ϕ^( )^k2 (A^( ) _ ρ1^k3 V^( ) _ ρ1^k1 - A^( ) _ ρ1^k1 V^( ) _ ρ1^k3)))

fields = {QuantumField[Particle[AxialVector[0], RenormalizationState[0]], LorentzIndex[μ1], SUNIndex[I1]][p1], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I2]][p2]}

{A^( ) _ μ _ 1^I _ 1, ϕ^( )^I _ 2}

melsimplified = IndicesCleanup[SUNReduce[FeynRule[llll, fields]]]

-f _ ϕ^(ó  ) p _ 2^μ _ 1 δ _ (I _ 1 I _ 2)^(3)

Converted by Mathematica  (July 10, 2003)