•Pπ S2

The leading order lagrangian in raw form:

Lagrangian[ChPT3[2]]

1/4 (f _ ϕ^(ó  ))^2 (< ÷„ '6 χ^† > + < χ '6 ÷„^† > + < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† >)

The evaluated lagrangian:

ll = ArgumentsSupply[Lagrangian[ChPT3[2]], x, RenormalizationState[0], ExpansionOrder -> 1, DropOrder -> 1, DiagonalToU -> True] ;

Redundant terms are discarded:

lll = DiscardTerms[ll, Retain -> {Particle[PseudoScalar[0] , RenormalizationState[0]] -> 1, Particle[PhiMeson , RenormalizationState[0]] -> 1, Particle[Scalar[2] , RenormalizationState[0]] -> 1}, Method -> Coefficient] // CycleUTraces // Simplify

0

Matrices are traced:

llle = ExpandU[lll, CommutatorReduce -> True] // Simplify

0

Indices are supplied:

$IsoIndicesCounter = 0 ;

llll = llle // IsoIndicesSupply // IndicesCleanup // CommutatorReduce

0

Calculation of the Feynman rule:

fields = {QuantumField[Particle[PseudoScalar[0], RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Scalar[2], RenormalizationState[0]], SUNIndex[I3]][p3]}

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

melsimplified = 0

0

Converted by Mathematica  (July 10, 2003)