•2πS

Lagrangian[ChPT2[4]] /. CouplingConstant[ChPT2[4], 1 | 2 | 3 | 7 | 9 | 10 | 11 | 12, ___][___] :> 0

L _ 6^( ) ((< ÷„ '6 χ^† > + < χ '6 ÷„^† >) '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 4^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 5^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 (÷„ '6 χ^† + χ '6 ÷„^†) > + L _ 8^( ) (< ÷„ '6 χ^† '6 ÷„ '6 χ^† > + < χ '6 ÷„^† '6 χ '6 ÷„^† >)

llt = UNMSplit[Lagrangian[ChPT2[4]] /. CouplingConstant[ChPT2[4], 1 | 2 | 3 | 7 | 9 | 10 | 11 | 12, ___][___] :> 0, x, DropOrder -> 2, DiagonalToU -> True] ;

llt // Length

4

lltt = (WriteString["stdout", "."] ; ArgumentsSupply[#, x, RenormalizationState[0], ExpansionOrder -> 2, DropOrder -> 2, DiagonalToU -> True]) & /@ llt ;

....

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

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

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

General :: stop : Further output of ArgumentsSupply :: \" argxpr \" will be suppressed during this calculation.

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

....

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

$IsoIndicesCounter = 0 ;

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

(8 !, _ 0^( ) s^( )^0 (-8 L _ 6^( ) (m _ π^(ó  ))^2 (π^( )^k1)^2 - 4 L _ 8^( ) (m _ π^(ó  ))^2 (π^( )^k1)^2 + (2 L _ 4^( ) + L _ 5^( )) (∂ _ τ1 π^( ) _ ó ^k1)^2))/(f _ π^(ó  ))^2

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

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

melsimplified = FeynRule[llll, fields] // Simplify // SUNReduce // IndicesCleanup // CommutatorReduce // Simplify

-(16 i (4 (2 L _ 6^( ) + L _ 8^( )) (m _ π^(ó  ))^2 + 2 L _ 4^( ) p _ 1 · p _ 2 + L _ 5^( ) p _ 1 · p _ 2) !, _ 0^( ) δ _ (0 I _ 3)^(2) δ _ (I _ 1 I _ 2)^(2))/(f _ π^(ó  ))^2

Converted by Mathematica  (July 10, 2003)