•Pϕϕϕ

ll = ArgumentsSupply[Lagrangian[ChPT3[2]], x, RenormalizationState[0], ExpansionOrder -> 3, DropOrder -> 3] ;

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

-(!, _ 0^( ) < Overscript[p^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >)/(12 f _ ϕ^(ó  )) - (!, _ 0^( ) < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[p^( ), ->] · Overscript[σ, ->] >)/(12 f _ ϕ^(ó  )) - (!, _ 0^( ) < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > p^( )^0)/(6 f _ ϕ^(ó  ))

llle = ExpandU[lll]

-((2 i Overscript[p^( ), ->] × Overscript[ϕ^( ), ->] ⊗ Overscript[ϕ^( ), ->] · Overscript[ϕ^( ), ->] + 2 Overscript[p^( ), ->] ⊗ Overscript[ϕ^( ), ->] ⊗ Overscript[ϕ^( ), ->] · Overscript[ϕ^( ), ->] + 4/3 Overscript[p^( ), ->] · Overscript[ϕ^( ), ->] Overscript[ϕ^( ), ->] · Overscript[ϕ^( ), ->]) !, _ 0^( ))/(12 f _ ϕ^(ó  )) - ((2 i Overscript[ϕ^( ), ->] ⊗ Overscript[ϕ^( ), ->] × Overscript[ϕ^( ), ->] · Overscript[p^( ), ->] + 2 Overscript[ϕ^( ), ->] ⊗ Overscript[ϕ^( ), ->] ⊗ Overscript[ϕ^( ), ->] · Overscript[p^( ), ->] + 4/3 Overscript[p^( ), ->] · Overscript[ϕ^( ), ->] Overscript[ϕ^( ), ->] · Overscript[ϕ^( ), ->]) !, _ 0^( ))/(12 f _ ϕ^(ó  )) - (Overscript[ϕ^( ), ->] ⊗ Overscript[ϕ^( ), ->] · Overscript[ϕ^( ), ->] p^( )^0 !, _ 0^( ))/(3 f _ ϕ^(ó  ))

$IsoIndicesCounter = 0 ;

llll = IsoIndicesSupply[llle] // SUNReduce // IndicesCleanup // Simplify

-(!, _ 0^( ) ϕ^( )^k2 (3 (2 d _ (k1 k2 k3)^(3) p^( )^0 + d _ (k1 k2 k5)^(3) (d _ (k3 k4 k5)^(3) + i f _ (k3 k4 k5)^(3)) p^( )^k4) ϕ^( )^k1 ϕ^( )^k3 + p^( )^k1 (4 ϕ^( )^k1 ϕ^( )^k2 + 3 d _ (k3 k4 k5)^(3) (d _ (k1 k2 k5)^(3) + i f _ (k1 k2 k5)^(3)) ϕ^( )^k3 ϕ^( )^k4)))/(18 f _ ϕ^(ó  ))

fields = {QuantumField[Particle[PseudoScalar[0], RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I3]][p3], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I4]][p4]}

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

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

-(2 i !, _ 0^( ) (3 d _ (I _ 1 I _ 4 k1)^(3) d _ (I _ 2 I _ 3 k1)^(3) + 3 d _ (I _ 1 I _ 3 k1)^(3) d _ (I _ 2 I _ 4 k1)^(3) + 3 d _ (I _ 1 I _ 2 k1)^(3) d _ (I _ 3 I _ 4 k1)^(3) + 9 d _ (I _ 2 I _ 3 I _ 4)^(3) δ _ (0 I _ 1)^(3) + 2 δ _ (I _ 1 I _ 4)^(3) δ _ (I _ 2 I _ 3)^(3) + 2 δ _ (I _ 1 I _ 3)^(3) δ _ (I _ 2 I _ 4)^(3) + 2 δ _ (I _ 1 I _ 2)^(3) δ _ (I _ 3 I _ 4)^(3)))/(9 f _ ϕ^(ó  ))

Converted by Mathematica  (July 10, 2003)