•Equations of motion

eomside0 = UTrace[-I/2 NM[UCommutator[HLeft[x], HRight[x]], UChiMinus[x] - 1/SUNN UTrace[UChiMinus[x]] + 2 CouplingConstant[ChPTVirtualPhotons2[2]]/DecayConstant[Pion]^2 * UCommutator[HLeft[x], HRight[x]]]] // NMExpand // Expand // CommutatorReduce

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

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 _ π^(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 >))/(f _ π^(ó  ))^2

eomside = eomside1 /. SUNN -> 2 /. su2qchalhamrule2 /. su2qchalhamrule3 /. su2qchalhamrule4 // NMExpand // Expand

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

eom = eomside - rha /. UTrace1[UMatrix[(UChiralSpurionRight | UChiralSpurionLeft)[]][x]] -> UTrace1[UMatrix[(UChiralSpurion)[]][x]] // Expand

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

List @@ eom

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

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

< ÷s _ μ_(÷„)^† '6 c _ μ_^R Q _ R '6 ÷„ '6 Q _ L > -> 1/2 i (-(8 i C^( ) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2)/(f _ π^(ó  ))^2 + (8 i C^( ) < Q >^2 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 - (4 i C^( ) < Q _ L '6 Q _ L > < Q >^2)/(f _ π^(ó  ))^2 - (4 i C^( ) < Q _ R '6 Q _ R > < Q >^2)/(f _ π^(ó  ))^2 + (8 i C^( ) < Q _ L '6 Q _ L > < Q _ R '6 Q _ R >)/(f _ π^(ó  ))^2 + 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 > - 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(÷„) >)

Converted by Mathematica  (July 10, 2003)