•ϕϕϕϕϕϕ

IsoVector[QuantumField[Particle[AxialVector[0], ___], ___], ___][_] := 0 ;

ll = ArgumentsSupply[Lagrangian[ChPT3[2]], x, RenormalizationState[0], ExpansionOrder -> 6, DropOrder -> 6] ;

$VeryVerbose = 2 ;

lll = DiscardTerms[ll, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 6}, CommutatorReduce -> False, Method -> Expand] ;

Using Method->Expand

Putting on dummy factors

Expanding NM products

Expanding DOT products

Expanding

Discarding terms

$VeryVerbose = 0 ;

DeclareUScalar[QuantumField[aa___, Particle[bb__], cc___][x_]]

Expand[lll] // Length

28

lala = ($IsoIndicesCounter = 0 ; PhiToFC[IsoIndicesSupply[#]]) & /@ Expand[lll] ;

lala // Length

28

lala[[1]]

-((m _ π^(ó  ))^2 ϕ^( )^i _ 1 ϕ^( )^i _ 2 ϕ^( )^i _ 3 ϕ^( )^i _ 4 ϕ^( )^i _ 5 ϕ^( )^i _ 6 < σ^i _ 1 . σ^i _ 2 . σ^i _ 3 . σ^i _ 4 . σ^i _ 5 . σ^i _ 6 >)/(4320 (f _ ϕ^(ó  ))^4)

DeclareNonCommutative[UMatrix[UGenerator[SUNIndex[j_], opt___], opts___]] ;

fields = FieldsSet[QuantumField[Particle[PhiMeson, RenormalizationState[0]]], ParticlesNumber -> 6]

{ϕ^( )^I _ 1, ϕ^( )^I _ 2, ϕ^( )^I _ 3, ϕ^( )^I _ 4, ϕ^( )^I _ 5, ϕ^( )^I _ 6}

ii = 0 ; res = CheckF[I * ((++ ii ; WriteString["stdout", ii, " "] ; CycleUTraces[FunctionalD[#, fields]]) & /@ lala), "6MesonVertex"] ;

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

res // LeafCount

275045

A test:

res // Expand // Length

5760

ii = 0 ; tmp = (If[IntegerQ[ii/100], WriteString["stdout", ii, " "]] ; ++ ii ; WriteOutUMatrices[SUNReduce[#, FullSimplify -> True]]) & /@ (Expand[res] /. {I1 -> 7, I2 -> 1, I3 -> 1, I4 -> 3, I5 -> 3, I6 -> 7}) ;

0 100 200 300 400 500 600 700 800 900

tmp // Simplify

1/(180 (f _ ϕ^(ó  ))^4) (i (-8 (m _ π^(ó  ))^2 + 4 (m _ K^+^(ó  ))^2 - 8 (m _ K^0^(ó  ))^2 + p _ 1 · p _ 2 + p _ 1 · p _ 3 + p _ 1 · p _ 4 + p _ 1 · p _ 5 - 4 p _ 1 · p _ 6 - 34 p _ 2 · p _ 3 + 16 p _ 2 · p _ 4 + 16 p _ 2 · p _ 5 + p _ 2 · p _ 6 + 16 p _ 3 · p _ 4 + 16 p _ 3 · p _ 5 + p _ 3 · p _ 6 - 34 p _ 4 · p _ 5 + p _ 4 · p _ 6 + p _ 5 · p _ 6))

Converted by Mathematica  (July 10, 2003)