•πA of first order in the chiral expansion

IsoVector[QuantumField[Particle[Vector[1], ___], ___], ___][_] := 0 ; <br /> QuantumField[Particle[Vector[1], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Vector[0], ___], ___], ___][_] := 0 ; <br /> QuantumField[Particle[Vector[0], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Scalar[2], ___], ___], ___][_] := 0 ; <br /> QuantumField[Particle[Scalar[2], ___], ___][_] := 0 ;

ll = ArgumentsSupply[Lagrangian[ChPTVirtualPhotons2[2]], 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] /. $Substitutions // Simplify

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

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

-2 f _ π^(ó  ) ∂ _ μ(Overscript[π^( ), ->]) · Overscript[A^( ) _ μ, ->]

llll = llle // IsoIndicesSupply // CommutatorReduce

-2 f _ π^(ó  ) ∂ _ μ π^( ) _ ó ^i _ 1 A^( ) _ μ^i _ 1

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}

amptree1 = (-I FeynRule[llll, fields]) // Simplify

2 i f _ π^(ó  ) p _ 2^μ _ 1 δ _ (I _ 1 I _ 2)

Converted by Mathematica  (July 10, 2003)