•4ϕS

ll = ArgumentsSupply[Lagrangian[ChPTWS3[2]], x, RenormalizationState[0], ExpansionOrder -> 4, DropOrder -> 4, DiagonalToU -> True] ;

Redundant terms are discarded:

lll = DiscardTerms[ll, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 4, Particle[Scalar[1], RenormalizationState[0]] -> 1}, CommutatorReduce -> True, Method -> Expand] // Simplify ;

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[PhiMeson, RenormalizationState[0]], SUNIndex[I4]][p4], QuantumField[Particle[Scalar[1], RenormalizationState[0]]][p5]}

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

lal = Expand[llll // PhiToFC] ;

melsimplified = ((WriteString["stdout", "."] ; Simplify[I * SUNReduce[SUNReduce[SUNReduce[FunctionalD[#, fields] // Contract]]]]) & /@ lal) ;

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

melsimplified1 = melsimplified /. DOT -> Times // Contract ;

melsimplified2 = Collect[melsimplified1, {_Pair}] ;

melsimplified2 // LeafCount

85007

melsimplified2 // Length

164

WriteString["stdout", "Total length: ", Length[melsimplified2]] ; melsimplified3 = CheckF[(WriteString["stdout", " leafs: ", LeafCount[#]] ; Collect[SUNReduce[SUNReduce[SUNReduce[SUNReduce[SUNReduce[#]]]]], {_DecayConstant, _CouplingConstant, _SU3Delta}]) & /@ Take[melsimplified2, {1, -1}], "4MesonsSVertexR.m"] ;

Total length: 164 leafs: 115 leafs: 115 leafs: 120 leafs: 120 leafs: 120 leafs: 265 leafs: 265 leafs: 265 leafs: 625 leafs: 625 leafs: 630 leafs: 630 leafs: 630 leafs: 241 leafs: 241 leafs: 77 leafs: 77 leafs: 77 leafs: 241 leafs: 241 leafs: 246 leafs: 246 leafs: 246 leafs: 270 leafs: 270 leafs: 270 leafs: 268 leafs: 268 leafs: 246 leafs: 246 leafs: 246 leafs: 103 leafs: 103 leafs: 103 leafs: 108 leafs: 108 leafs: 108 leafs: 106 leafs: 106 leafs: 201 leafs: 201 leafs: 206 leafs: 206 leafs: 206 leafs: 83 leafs: 83 leafs: 253 leafs: 253 leafs: 623 leafs: 623 leafs: 88 leafs: 88 leafs: 88 leafs: 253 leafs: 253 leafs: 258 leafs: 258 leafs: 258 leafs: 270 leafs: 270 leafs: 270 leafs: 623 leafs: 623 leafs: 628 leafs: 628 leafs: 628 leafs: 625 leafs: 625 leafs: 258 leafs: 258 leafs: 258 leafs: 630 leafs: 630 leafs: 630 leafs: 628 leafs: 628 leafs: 628 leafs: 279 leafs: 279 leafs: 279 leafs: 277 leafs: 277 leafs: 2614 leafs: 3219 leafs: 2937 leafs: 3015 leafs: 3108 leafs: 3086 leafs: 263 leafs: 263 leafs: 263 leafs: 623 leafs: 623 leafs: 628 leafs: 628 leafs: 628 leafs: 625 leafs: 625 leafs: 630 leafs: 630 leafs: 630 leafs: 625 leafs: 625 leafs: 630 leafs: 630 leafs: 630 leafs: 277 leafs: 277 leafs: 623 leafs: 623 leafs: 623 leafs: 623 leafs: 628 leafs: 628 leafs: 628 leafs: 628 leafs: 628 leafs: 628 leafs: 275 leafs: 275 leafs: 275 leafs: 623 leafs: 623 leafs: 628 leafs: 628 leafs: 628 leafs: 625 leafs: 625 leafs: 625 leafs: 625 leafs: 630 leafs: 630 leafs: 630 leafs: 630 leafs: 630 leafs: 630 leafs: 625 leafs: 625 leafs: 630 leafs: 630 leafs: 630 leafs: 282 leafs: 282 leafs: 284 leafs: 284 leafs: 284 leafs: 275 leafs: 275 leafs: 275 leafs: 623 leafs: 623 leafs: 628 leafs: 628 leafs: 628 leafs: 623 leafs: 623 leafs: 628 leafs: 628 leafs: 628 leafs: 625 leafs: 625 leafs: 630 leafs: 630 leafs: 630

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

(SUNReduce[#, Explicit -> True, HoldSums -> False] & /@ (melsimplified /. {I1 -> 6, I2 -> 3, I3 -> 3, I4 -> 3} // Expand)) // Simplify

-(i (3 c _ 5^( ) (m _ K^0^(ó  ))^2 + 2 c _ 2^( ) (p _ 1 · p _ 2 + p _ 1 · p _ 3 + p _ 1 · p _ 4 - p _ 2 · p _ 3 - p _ 2 · p _ 4 - p _ 3 · p _ 4)))/(3 (f _ ϕ^(ó  ))^4)

(SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ (melsimplified /. {I1 -> 6, I2 -> 3, I3 -> 3, I4 -> 3} // Expand)) // Simplify

-(i (3 c _ 5^( ) (m _ K^0^(ó  ))^2 + 2 c _ 2^( ) (p _ 1 · p _ 2 + p _ 1 · p _ 3 + p _ 1 · p _ 4 - p _ 2 · p _ 3 - p _ 2 · p _ 4 - p _ 3 · p _ 4)))/(3 (f _ ϕ^(ó  ))^4)

Converted by Mathematica  (July 10, 2003)