•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 /. SUNN -> 3 /. $Substitutions // UReduce[#, SMMToMM -> True] & // NMExpand // Expand

1/6 i < ÷„^† '6 χ >^2 - 1/3 i < χ^† '6 ÷„ > < ÷„^† '6 χ > + 1/6 i < χ^† '6 ÷„ >^2 + i < χ^† '6 χ > - 1/2 i < ÷„^† '6 χ '6 ÷„^† '6 χ > - 1/2 i < χ^† '6 ÷„ '6 χ^† '6 ÷„ >

-I * eomside // Expand

1/6 < ÷„^† '6 χ >^2 - 1/3 < χ^† '6 ÷„ > < ÷„^† '6 χ > + 1/6 < χ^† '6 ÷„ >^2 + < χ^† '6 χ > - 1/2 < ÷„^† '6 χ '6 ÷„^† '6 χ > - 1/2 < χ^† '6 ÷„ '6 χ^† '6 ÷„ >

-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(÷„)^† >

% // InputForm

-UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]],
    CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ]]]] -
UTrace1[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ]]],
   CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]] -
UTrace1[NM[Adjoint[MM[x]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]],
   Adjoint[UMatrix[UChi[]][x]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]] -
UTrace1[NM[MM[x], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]],
   UMatrix[UChi[]][x], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]]]

%% // InputForm

-UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]],
    CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ]]]] -
UTrace1[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ]]],
   CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]] -
UTrace1[NM[Adjoint[MM[x]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]],
   Adjoint[UMatrix[UChi[]][x]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]] -
UTrace1[NM[MM[x], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]],
   UMatrix[UChi[]][x], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]]]

$EOMRules = {UTrace1[NM[Adjoint[MM[x_]], CovariantFieldDerivative[MM[x_], x_, LorentzIndex[μ_]], Adjoint[UMatrix[UChi[]][x_]], CovariantFieldDerivative[MM[x_], x, LorentzIndex[μ_]]]] -> -(UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]^2/6 - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]] * UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]])/3 + UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]]^2/6 + UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChi[]][x]]] - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x], Adjoint[MM[x]], UMatrix[UChi[]][x]]]/2 - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x], Adjoint[UMatrix[UChi[]][x]], MM[x]]]/2 - (-UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ]]]] - UTrace1[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]] - UTrace1[NM[MM[x], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], UMatrix[UChi[]][x], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]]])), UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[μ_]]], MM[x_], Adjoint[UMatrix[UChi[]][x_]], CovariantFieldDerivative[MM[x_], x, LorentzIndex[μ_]]]] -> (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]^2/6 - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]] * UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]])/3 + UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]]^2/6 + UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChi[]][x]]] - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x], Adjoint[MM[x]], UMatrix[UChi[]][x]]]/2 - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x], Adjoint[UMatrix[UChi[]][x]], MM[x]]]/2 - (-UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ]]]] - UTrace1[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]] - UTrace1[NM[MM[x], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], UMatrix[UChi[]][x], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]]]))}

{< ÷„^† '6 ÷s _ μ_(÷„) '6 χ^† '6 ÷s _ μ_(÷„) > -> -1/6 < ÷„^† '6 χ >^2 + 1/3 < χ^† '6 ÷„ > < ÷„^† '6 χ > - 1/6 < χ^† '6 ÷„ >^2 - < ÷s _ μ(÷„)^† '6 ÷s _ μ(χ) > - < ÷s _ μ(χ)^† '6 ÷s _ μ(÷„) > - < χ^† '6 χ > + 1/2 < ÷„^† '6 χ '6 ÷„^† '6 χ > + 1/2 < χ^† '6 ÷„ '6 χ^† '6 ÷„ > - < ÷„ '6 ÷s _ μ(÷„)^† '6 χ '6 ÷s _ μ(÷„)^† >, < ÷s _ μ_(÷„)^† '6 ÷„ '6 χ^† '6 ÷s _ μ_(÷„) > -> 1/6 < ÷„^† '6 χ >^2 - 1/3 < χ^† '6 ÷„ > < ÷„^† '6 χ > + 1/6 < χ^† '6 ÷„ >^2 + < ÷s _ μ(÷„)^† '6 ÷s _ μ(χ) > + < ÷s _ μ(χ)^† '6 ÷s _ μ(÷„) > + < χ^† '6 χ > - 1/2 < ÷„^† '6 χ '6 ÷„^† '6 χ > - 1/2 < χ^† '6 ÷„ '6 χ^† '6 ÷„ > + < ÷„ '6 ÷s _ μ(÷„)^† '6 χ '6 ÷s _ μ(÷„)^† >}

Converted by Mathematica  (July 10, 2003)