•3πP

ll = ArgumentsSupply[Lagrangian[ChPT2[2]], x, RenormalizationState[0], ExpansionOrder -> 3, DropOrder -> 3] ;

lll = DiscardTerms[ll, Retain -> {Particle[PseudoScalar[0] , RenormalizationState[0]] -> 1, Particle[Pion , RenormalizationState[0]] -> 3}, CommutatorReduce -> True] ;

llle = ExpandU[lll]

-(Overscript[p^( ), ->] · Overscript[π^( ), ->] Overscript[π^( ), ->] · Overscript[π^( ), ->] !, _ 0^( ))/(3 f _ π^(ó  ))

$IsoIndicesCounter = 0 ;

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

-(!, _ 0^( ) p^( )^k1 π^( )^k1 (π^( )^k2)^2)/(3 f _ π^(ó  ))

fields = {QuantumField[Particle[PseudoScalar[0], 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]}

{p^( )^I _ 1, π^( )^I _ 2, π^( )^I _ 3, π^( )^I _ 4}

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

-(2 i !, _ 0^( ) (δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) + δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) + δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2)))/(3 f _ π^(ó  ))

Converted by Mathematica  (July 10, 2003)