•Pπ S2

IsoVector[QuantumField[___, Particle[AxialVector[0], ___], ___], ___][_] := 0 ; <br /> QuantumField[___, Particle[AxialVector[0], ___], ___][_] := 0 ;

Lagrangian[ChPT3[4]]

L _ 7^( ) ((< χ '6 ÷„^† > - < ÷„ '6 χ^† >) '6 (< χ '6 ÷„^† > - < ÷„ '6 χ^† >)) + L _ 6^( ) ((< ÷„ '6 χ^† > + < χ '6 ÷„^† >) '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 4^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 1^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 < ÷s _ ν(÷„) '6 ÷s _ ν(÷„)^† >) + L _ 2^( ) (< ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† > '6 < ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† >) + H _ 2^( ) < χ^† '6 χ > + H _ 1^( ) (< L _ (μ ν) '6 L _ (μ ν) > + < R _ (μ ν) '6 R _ (μ ν) >) + L _ 5^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 (÷„ '6 χ^† + χ '6 ÷„^†) > + i L _ 9^( ) (< L _ (μ ν) '6 ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† > + < R _ (μ ν) '6 ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) >) + L _ 8^( ) (< ÷„ '6 χ^† '6 ÷„ '6 χ^† > + < χ '6 ÷„^† '6 χ '6 ÷„^† >) + L _ 3^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) '6 ÷s _ ν(÷„)^† > + L _ 10^( ) < L _ (μ ν) '6 ÷„ '6 R _ (μ ν) '6 ÷„^† >

llt = UNMSplit[Lagrangian[ChPT3[4]], x, DropOrder -> 1, DiagonalToU -> True] ;

lllt = Select[llt // NMExpand // Expand, (! FreeQ[#, UChiMatrix] &)] ;

lllt // Length

21

lltt = ArgumentsSupply[lllt, x, RenormalizationState[0], ExpansionOrder -> 1, DropOrder -> 1, DiagonalToU -> True] ;

ArgumentsSupply :: argxpr : Warning : The argument x is already in the expression.

lltt // Length

21

llltt = (WriteString["stdout", "."] ; (# /. UTrace1 -> tr // NMExpand) /. tr -> UTrace // ExpandAll // NMExpand // Expand) & /@ lltt ;

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

llltt // Length

338

lll = (WriteString["stdout", "."] ; DiscardTerms[#, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 1, Particle[PseudoScalar[0], RenormalizationState[0]] -> 1, Particle[Scalar[2], RenormalizationState[0]] -> 1}, Method -> Expand]) & /@ llltt ;

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

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

$IsoIndicesCounter = 0 ;

llll = llle // IsoIndicesSupply // SUNReduce // IndicesCleanup // Simplify ;

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 = FeynRule[llll, fields] // SUNReduce[#, FullReduce -> True] & // IndicesCleanup // CommutatorReduce // Simplify

(64 i (!, _ 0^( ))^2 (L _ 8^( ) (d _ (I _ 1 I _ 2 I _ 3)^(3) + δ _ (0 I _ 3)^(3) δ _ (I _ 1 I _ 2)^(3) + δ _ (0 I _ 1)^(3) δ _ (I _ 2 I _ 3)^(3)) + 3 (L _ 6^( ) δ _ (0 I _ 3)^(3) δ _ (I _ 1 I _ 2)^(3) + L _ 7^( ) δ _ (0 I _ 1)^(3) δ _ (I _ 2 I _ 3)^(3))))/f _ ϕ^(ó  )

Converted by Mathematica  (July 10, 2003)