•Equations of motion

eomside0 = UTrace[-I/2 NM[UChiMinus[x], UChiMinus[x] - 1/SUNN UTrace[UChiMinus[x]]]] // NMExpand // Expand // CommutatorReduce

(i < χ _ - >^2)/(2 N) - 1/2 i < χ _ - '6 χ _ - >

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

(i (< ÷„^† '6 χ > - < χ^† '6 ÷„ >)^2)/(2 N) - 1/2 i (-2 < χ^† '6 χ > + < ÷„^† '6 χ '6 ÷„^† '6 χ > + < χ^† '6 ÷„ '6 χ^† '6 ÷„ >)

eomside = eomside1 /. detChiRule /. SUNN -> 2 /. $Substitutions // UReduce[#, SMMToMM -> True] & // NMExpand // Expand

-1/4 i < ÷„^† '6 χ >^2 - 1/2 i < χ^† '6 ÷„ > < ÷„^† '6 χ > - 1/4 i < χ^† '6 ÷„ >^2 + 1/2 i {χ^†} + (i {χ})/2 + i < χ^† '6 χ >

-I * eomside // Expand

-1/4 < ÷„^† '6 χ >^2 - 1/2 < χ^† '6 ÷„ > < ÷„^† '6 χ > - 1/4 < χ^† '6 ÷„ >^2 + {χ^†}/2 + {χ}/2 + < χ^† '6 χ >

-I * rh // Expand

-< ÷s _ μ(÷„)^† '6 ÷s _ μ(χ) > - < ÷s _ μ(χ)^† '6 ÷s _ μ(÷„) > - < ÷„^† '6 ÷s _ μ(÷„) '6 χ^† '6 ÷s _ μ(÷„) > - < ÷„ '6 ÷s _ μ(÷„)^† '6 χ '6 ÷s _ μ(÷„)^† >

eomRule = UTrace1[NM[Adjoint[MM[x_]], CovariantFieldDerivative[MM[x_], x_, LorentzIndex[μ_]], Adjoint[UMatrix[UChi[chopts___]][x_]], CovariantFieldDerivative[MM[x_], x_, LorentzIndex[μ_]]]] + UTrace1[NM[MM[x_], Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[μ_]]], UMatrix[UChi[chopts___]][x_], Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[μ_]]]]] -> -UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, LorentzIndex[μ]]]] - UTrace1[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, LorentzIndex[μ]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]] - 1/2 Det[Adjoint[UMatrix[UChi[chopts]][x]]] - 1/2 Det[UMatrix[UChi[chopts]][x]] + 1/4 UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]]^2 + 1/2 UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]] UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]] + 1/4 UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]]^2 - UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], UMatrix[UChi[chopts]][x]]]

< ÷„^† '6 ÷s _ μ_(÷„) '6 χ^† '6 ÷s _ μ_(÷„) > + < ÷„ '6 ÷s _ μ_(÷„)^† '6 χ '6 ÷s _ μ_(÷„)^† > -> 1/4 < ÷„^† '6 χ >^2 + 1/2 < χ^† '6 ÷„ > < ÷„^† '6 χ > + 1/4 < χ^† '6 ÷„ >^2 - {χ^†}/2 - {χ}/2 - < ÷s _ μ(÷„)^† '6 ÷s _ μ(χ) > - < ÷s _ μ(χ)^† '6 ÷s _ μ(÷„) > - < χ^† '6 χ >


Converted by Mathematica  (July 10, 2003)