•ϕϕϕϕ

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

ll = ArgumentsSupply[Lagrangian[ChPT3[2]], x, RenormalizationState[0], ExpansionOrder -> 4, DropOrder -> 4] ;

$VeryVerbose = 2 ;

lll = DiscardTerms[ll, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 4}, Method -> Expand] ;

Using Method->Expand

Putting on dummy factors

Expanding NM products

Expanding DOT products

Expanding

Discarding terms

lll

(< Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > (m _ π^(ó  ))^2)/(144 (f _ ϕ^(ó  ))^2) + (< Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^8 > (m _ π^(ó  ))^2)/(48 3^(1/2) (f _ ϕ^(ó  ))^2) + (< σ^8 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > (m _ π^(ó  ))^2)/(48 3^(1/2) (f _ ϕ^(ó  ))^2) + ((m _ K^+^(ó  ))^2 < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >)/(144 (f _ ϕ^(ó  ))^2) + ((m _ K^0^(ó  ))^2 < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >)/(144 (f _ ϕ^(ó  ))^2) - < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] >/(24 (f _ ϕ^(ó  ))^2) + < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] >/(48 (f _ ϕ^(ó  ))^2) + < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >/(16 (f _ ϕ^(ó  ))^2) - < ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] >/(48 (f _ ϕ^(ó  ))^2) + < ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >/(48 (f _ ϕ^(ó  ))^2) - < ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 ∂ _ μ(Overscript[ϕ^( ), ->]) · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >/(24 (f _ ϕ^(ó  ))^2) + ((m _ K^+^(ó  ))^2 < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^3 >)/(96 (f _ ϕ^(ó  ))^2) - ((m _ K^0^(ó  ))^2 < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^3 >)/(96 (f _ ϕ^(ó  ))^2) - ((m _ K^+^(ó  ))^2 < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^8 >)/(96 3^(1/2) (f _ ϕ^(ó  ))^2) - ((m _ K^0^(ó  ))^2 < Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^8 >)/(96 3^(1/2) (f _ ϕ^(ó  ))^2) + ((m _ K^+^(ó  ))^2 < σ^3 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >)/(96 (f _ ϕ^(ó  ))^2) - ((m _ K^0^(ó  ))^2 < σ^3 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >)/(96 (f _ ϕ^(ó  ))^2) - ((m _ K^+^(ó  ))^2 < σ^8 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >)/(96 3^(1/2) (f _ ϕ^(ó  ))^2) - ((m _ K^0^(ó  ))^2 < σ^8 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >)/(96 3^(1/2) (f _ ϕ^(ó  ))^2)

•Method 1: Explicit traces (only Kronecker deltas)
•Method 2: Non-explicit traces (Kronecker deltas, f's and d's)
•A few checks:

Converted by Mathematica  (July 10, 2003)