•Equations of motion

eomside0 = UTrace[-I/2 NM[NM[HLeft[x], HRight[x]] - NM[HRight[x], HLeft[x]], UChiMinus[x] - 1/SUNN UTrace[UChiMinus[x]] + 2 CouplingConstant[ChPTVirtualPhotons3[2]]/DecayConstant[PhiMeson]^2 * UCommutator[HLeft[x], HRight[x]]]] // NMExpand // Expand // CommutatorReduce // CycleUTraces

-1/2 i < H _ L '6 H _ R '6 χ _ - > + 1/2 i < H _ L '6 χ _ - '6 H _ R > + (2 i C^( ) < H _ L '6 H _ L '6 H _ R '6 H _ R >)/(f _ ϕ^(ó  ))^2 - (2 i C^( ) < H _ L '6 H _ R '6 H _ L '6 H _ R >)/(f _ ϕ^(ó  ))^2

eomside1 = eomside0 /. $Substitutions // UReduce[#, SMMToMM -> True] &

1/2 i (-< ÷„^† '6 χ '6 Q _ L '6 Q _ L > + < ÷„^† '6 Q _ R '6 χ '6 Q _ L > + < ÷„^† '6 Q _ R '6 Q _ R '6 χ > + < χ^† '6 ÷„ '6 Q _ L '6 Q _ L > + < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > - < χ^† '6 Q _ R '6 Q _ R '6 ÷„ > - < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > - < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R >) - 1/2 i (-< ÷„^† '6 χ '6 Q _ L '6 Q _ L > - < ÷„^† '6 Q _ R '6 χ '6 Q _ L > + < ÷„^† '6 Q _ R '6 Q _ R '6 χ > + < χ^† '6 ÷„ '6 Q _ L '6 Q _ L > - < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > - < χ^† '6 Q _ R '6 Q _ R '6 ÷„ > + < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > + < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R >) + (2 i C^( ) (< Q _ L '6 Q _ L '6 Q _ L '6 Q _ L > + < Q _ R '6 Q _ R '6 Q _ R '6 Q _ R > - 2 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >))/(f _ ϕ^(ó  ))^2 - 1/(f _ ϕ^(ó  ))^2 (2 i C^( ) (< Q _ L '6 Q _ L '6 Q _ L '6 Q _ L > + < Q _ R '6 Q _ R '6 Q _ R '6 Q _ R > - 4 < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L > + 2 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >))

eomside = eomside1 // UReduce[#, SMMToMM -> True] & // NMExpand // Expand

i < ÷„^† '6 Q _ R '6 χ '6 Q _ L > + i < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > - i < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > + (8 i C^( ) < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L >)/(f _ ϕ^(ó  ))^2 - i < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R > - (8 i C^( ) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ ϕ^(ó  ))^2

eom = eomside - rha // Expand

2 i < ÷s _ μ(÷„)^† '6 c _ μ^R Q _ R '6 ÷„ '6 Q _ L > + 4 i < ÷s _ μ(÷„)^† '6 Q _ R '6 ÷s _ μ(÷„) '6 Q _ L > + 2 i < ÷s _ μ(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ^L Q _ L > + 2 i < ÷„^† '6 c _ μ^R Q _ R '6 ÷s _ μ(÷„) '6 Q _ L > + 2 i < ÷„^† '6 Q _ R '6 ÷s _ μ(÷„) '6 c _ μ^L Q _ L > + i < ÷„^† '6 Q _ R '6 χ '6 Q _ L > + i < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > - i < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > + (8 i C^( ) < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L >)/(f _ ϕ^(ó  ))^2 - i < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R > + 2 i < Q _ L '6 ÷s _ μ(÷„)^† '6 ÷„ '6 ÷s _ μ(÷„)^† '6 Q _ R '6 ÷„ > + 2 i < Q _ L '6 ÷„^† '6 Q _ R '6 ÷s _ μ(÷„) '6 ÷„^† '6 ÷s _ μ(÷„) > - (8 i C^( ) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ ϕ^(ó  ))^2

List @@ eom

{2 i < ÷s _ μ(÷„)^† '6 c _ μ^R Q _ R '6 ÷„ '6 Q _ L >, 4 i < ÷s _ μ(÷„)^† '6 Q _ R '6 ÷s _ μ(÷„) '6 Q _ L >, 2 i < ÷s _ μ(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ^L Q _ L >, 2 i < ÷„^† '6 c _ μ^R Q _ R '6 ÷s _ μ(÷„) '6 Q _ L >, 2 i < ÷„^† '6 Q _ R '6 ÷s _ μ(÷„) '6 c _ μ^L Q _ L >, i < ÷„^† '6 Q _ R '6 χ '6 Q _ L >, i < χ^† '6 Q _ R '6 ÷„ '6 Q _ L >, -i < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L >, (8 i C^( ) < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L >)/(f _ ϕ^(ó  ))^2, -i < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R >, 2 i < Q _ L '6 ÷s _ μ(÷„)^† '6 ÷„ '6 ÷s _ μ(÷„)^† '6 Q _ R '6 ÷„ >, 2 i < Q _ L '6 ÷„^† '6 Q _ R '6 ÷s _ μ(÷„) '6 ÷„^† '6 ÷s _ μ(÷„) >, -(8 i C^( ) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ ϕ^(ó  ))^2}

eomRule1 = (-I * 1/2 * eom[[1]] /. {μ -> μ_, x -> x_}) -> (I * 1/2 * Plus @@ Drop[eom, {1}] // Expand)

< ÷s _ μ_(÷„)^† '6 c _ μ_^R Q _ R '6 ÷„ '6 Q _ L > -> -2 < ÷s _ μ(÷„)^† '6 Q _ R '6 ÷s _ μ(÷„) '6 Q _ L > - < ÷s _ μ(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ^L Q _ L > - < ÷„^† '6 c _ μ^R Q _ R '6 ÷s _ μ(÷„) '6 Q _ L > - < ÷„^† '6 Q _ R '6 ÷s _ μ(÷„) '6 c _ μ^L Q _ L > - 1/2 < ÷„^† '6 Q _ R '6 χ '6 Q _ L > - 1/2 < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > + 1/2 < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > - (4 C^( ) < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L >)/(f _ ϕ^(ó  ))^2 + 1/2 < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R > - < Q _ L '6 ÷s _ μ(÷„)^† '6 ÷„ '6 ÷s _ μ(÷„)^† '6 Q _ R '6 ÷„ > - < Q _ L '6 ÷„^† '6 Q _ R '6 ÷s _ μ(÷„) '6 ÷„^† '6 ÷s _ μ(÷„) > + (4 C^( ) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ ϕ^(ó  ))^2

Converted by Mathematica  (July 10, 2003)