•Four-vertex

IsoVector[QuantumField[Particle[AxialVector[0], ___], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Vector[0], ___], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Scalar[1 | 2], ___], ___], ___][_] := 0 ; QuantumField[Particle[Scalar[1 | 2], ___], ___][_] := 0 ; QuantumField[Particle[PseudoScalar[0], ___], ___][_] := 0 ;

lag = Lagrangian[ChPT2[4]] /. CouplingConstant[ChPT2[4], _ ? (FreeQ[#, 1 | 2 | 3 | 4 | 5 | 6 | 8] &), ___] -> 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 _ 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(÷„)^† >) + L _ 5^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 (÷„ '6 χ^† + χ '6 ÷„^†) > + 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(÷„)^† >

ll = (WriteString["stdout", "."] ; UNMSplit[#, x, DropOrder -> 4]) & /@ lag ;

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

lll = ArgumentsSupply[ll, x, RenormalizationState[0], ExpansionOrder -> 1, DropOrder -> 4] ;

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

llle = ExpandU[lll] // CommutatorReduce // Simplify

1/(3 (f _ π^(ó  ))^4) (2 (3 H _ 2^( ) (f _ π^(ó  ))^4 (m _ π^(ó  ))^4 + 8 L _ 6^( ) (Overscript[π^( ), ->] · Overscript[π^( ), ->])^2 (m _ π^(ó  ))^4 + 4 L _ 8^( ) (Overscript[π^( ), ->] · Overscript[π^( ), ->])^2 (m _ π^(ó  ))^4 + 4 L _ 4^( ) (Overscript[π^( ), ->] · ∂ _ μ(Overscript[π^( ), ->]))^2 (m _ π^(ó  ))^2 + 2 L _ 5^( ) (Overscript[π^( ), ->] · ∂ _ μ(Overscript[π^( ), ->]))^2 (m _ π^(ó  ))^2 - 10 L _ 4^( ) Overscript[π^( ), ->] · Overscript[π^( ), ->] ∂ _ μ(Overscript[π^( ), ->]) · ∂ _ μ(Overscript[π^( ), ->]) (m _ π^(ó  ))^2 - 5 L _ 5^( ) Overscript[π^( ), ->] · Overscript[π^( ), ->] ∂ _ μ(Overscript[π^( ), ->]) · ∂ _ μ(Overscript[π^( ), ->]) (m _ π^(ó  ))^2 + 6 L _ 2^( ) (∂ _ μ(Overscript[π^( ), ->]) · ∂ _ ν(Overscript[π^( ), ->]))^2 + 6 L _ 1^( ) ∂ _ μ(Overscript[π^( ), ->]) · ∂ _ μ(Overscript[π^( ), ->]) ∂ _ ν(Overscript[π^( ), ->]) · ∂ _ ν(Overscript[π^( ), ->]) + 3 L _ 3^( ) ∂ _ μ(Overscript[π^( ), ->]) · ∂ _ μ(Overscript[π^( ), ->]) ∂ _ ν(Overscript[π^( ), ->]) · ∂ _ ν(Overscript[π^( ), ->])))

$IsoIndicesCounter = 0 ;

llll = llle // IsoIndicesSupply // IndicesCleanup // FullSimplify

1/(3 (f _ π^(ó  ))^4) (2 ((3 H _ 2^( ) (f _ π^(ó  ))^4 + 4 (2 L _ 6^( ) + L _ 8^( )) (π^( )^k1)^2 (π^( )^k2)^2) (m _ π^(ó  ))^2 - 5 (2 L _ 4^( ) + L _ 5^( )) (π^( )^k1)^2 (∂ _ τ1 π^( ) _ ó ^k2)^2 + 2 (2 L _ 4^( ) + L _ 5^( )) π^( )^k1 π^( )^k2 ∂ _ τ1 π^( ) _ ó ^k1 ∂ _ τ1 π^( ) _ ó ^k2) (m _ π^(ó  ))^2 + 6 (2 L _ 1^( ) + L _ 3^( )) (∂ _ τ1 π^( ) _ ó ^k1)^2 (∂ _ τ2 π^( ) _ ó ^k2)^2 + 12 L _ 2^( ) ∂ _ τ1 π^( ) _ ó ^k1 ∂ _ τ1 π^( ) _ ó ^k2 ∂ _ τ2 π^( ) _ ó ^k1 ∂ _ τ2 π^( ) _ ó ^k2)

fields = FieldsSet[QuantumField[Particle[Pion, RenormalizationState[0]]]]

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

melsimplified = FeynRule[llll, fields] // FullSimplify

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

Converted by Mathematica  (July 10, 2003)