•3ϕS

ll = ArgumentsSupply[Lagrangian[ChPTWS3[2]], x, RenormalizationState[0], ExpansionOrder -> 3, DropOrder -> 3, DiagonalToU -> True] ;

Redundant terms are discarded:

lll = DiscardTerms[ll, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 3}, CommutatorReduce -> True, Method -> Coefficient] // Simplify

-1/(18 (f _ ϕ^(ó  ))^3) (i s^( ) (9 c _ 2^( ) (< σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] > - < σ^6 '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >) + c _ 5^( ) (-2 3^(1/2) < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^8 > (m _ π^(ó  ))^2 + 2 3^(1/2) < σ^6 '6 σ^8 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > (m _ π^(ó  ))^2 + 3 (m _ K^0^(ó  ))^2 < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^3 > + 3^(1/2) (m _ K^0^(ó  ))^2 < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^8 > - 3 (m _ K^0^(ó  ))^2 < σ^6 '6 σ^3 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > - 3^(1/2) (m _ K^0^(ó  ))^2 < σ^6 '6 σ^8 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > + (m _ K^+^(ó  ))^2 (-3 < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^3 > + 3^(1/2) < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^8 > + 3 < σ^6 '6 σ^3 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > - 3^(1/2) < σ^6 '6 σ^8 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >) - 6 i !, _ 0^( ) (< σ^6 '6 Overscript[p^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > + < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[p^( ), ->] · Overscript[σ, ->] > - i < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[s^( ), ->] · Overscript[σ, ->] > + i < σ^6 '6 Overscript[s^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > + 2 < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > p^( )^0))))

Generator matrices are traced:

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

Indices are supplied:

$IsoIndicesCounter = 0 ;

llll = llle // IsoIndicesSupply // IndicesCleanup ;

Calculation of the Feynman rule:

fields = {QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I3]][p3], QuantumField[Particle[Scalar[1], RenormalizationState[0]]][p4]}

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

lal = Expand[llll] ;

lal // Length

125

melsimplified = If[Head[lal] == Plus, Plus @@ ((WriteString["stdout", "."] ; IndicesCleanup[SUNReduce[FeynRule[#, fields], FullReduce -> True]]) & /@ (List @@ lal))] ;

.............................................................................................................................

A check that two different evaluations with specific components give the same result:

(SUNReduce[#, Explicit -> True, HoldSums -> False] & /@ (melsimplified /. {I1 -> 7, I2 -> 3, I3 -> 3} // Expand)) // Simplify

(i (3 c _ 2^( ) (p _ 1 · p _ 2 + p _ 1 · p _ 3 - 2 p _ 2 · p _ 3) + 4 c _ 5^( ) ((m _ K^+^(ó  ))^2 - (m _ π^(ó  ))^2)))/(3 (f _ ϕ^(ó  ))^3)

(SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ (melsimplified /. {I1 -> 7, I2 -> 3, I3 -> 3} // Expand)) // Simplify

(i (3 c _ 2^( ) (p _ 1 · p _ 2 + p _ 1 · p _ 3 - 2 p _ 2 · p _ 3) + 4 c _ 5^( ) ((m _ K^+^(ó  ))^2 - (m _ π^(ó  ))^2)))/(3 (f _ ϕ^(ó  ))^3)

Converted by Mathematica  (July 10, 2003)