•Two-vertex

lag = Lagrangian[ChPT2[4]] /. CouplingConstant[ChPT2[4], 1 | 2 | 3 | 6 | 7 | 8 | 9 | 10 | 11 | 12, ___][___] -> 0

L _ 4^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 5^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 (÷„ '6 χ^† + χ '6 ÷„^†) >

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

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

(2 (2 L _ 4^( ) + L _ 5^( )) (m _ π^(ó  ))^2 (< ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] > + < Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] >))/f _ π^(ó  )

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

(8 (2 L _ 4^( ) + L _ 5^( )) ∂ _ μ(Overscript[π^( ), ->]) · Overscript[A^( ) _ μ, ->] (m _ π^(ó  ))^2)/f _ π^(ó  )

$IsoIndicesCounter = 0 ;

llll = llle // IsoIndicesSupply // CommutatorReduce

(8 (2 L _ 4^( ) + L _ 5^( )) (m _ π^(ó  ))^2 ∂ _ μ π^( ) _ ó ^i _ 1 A^( ) _ μ^i _ 1)/f _ π^(ó  )

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

{A^( ) _ μ _ 1^I _ 1, π^( )^I _ 2}

amptree3 = (-I FeynRule[llll, fields]) // Simplify

-(8 i (2 L _ 4^( ) + L _ 5^( )) p _ 2^μ _ 1 (m _ π^(ó  ))^2 δ _ (I _ 1 I _ 2))/f _ π^(ó  )

Converted by Mathematica  (July 10, 2003)