•Method 1: Explicit traces (only Kronecker deltas)

lll[[1]]

((m _ π^(ó  ))^2 < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >)/(144 (f _ ϕ^(ó  ))^2)

lag = (lll // WriteOutIsoVectors // WriteOutUMatrices) /. NM -> Times // Simplify ;

fields = FieldsSet[QuantumField[Particle[PhiMeson, RenormalizationState[0]]]]

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

Length[Expand[lag]]

245

res = ((WriteString["stdout", "."] ; FunctionalD[PhiToFC[#], fields]) & /@ Expand[lag]) ;

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

res1 = Collect[Expand[res], {_DecayConstant, _SUNDelta, _Pair, _ParticleMass}] ;

res1 // LeafCount

46796

Converted by Mathematica  (July 10, 2003)