Subject: Dirac Trace Problem
To: feyncalc@feyncalc.org
From: Alaksiej Kacanovic <noreply@feyncalc.org>
Replyto: feyncalc@feyncalc.org
I have the problem, I try multiply two terms with gamma matrices
DD = (I GS[p] - g GA[\[Mu]].QuantumField[A, \[Mu]] - m -
QuantumField[\[Sigma]] - I GA[5] SUNT[a].QuantumField[\[Pi]f, a])
DDh = (-I GA[0].GS[p].GA[0] -
g GA[0].GA[\[Nu]].GA[0].QuantumField[A, \[Nu]] - m -
QuantumField[\[Sigma]] + I GA[5] SUNT[b].QuantumField[\[Pi]f, b])
and calculate Dirac and SU(N) traces. So I enter
hhh = DDh.DD
hhh2 = DiracTrace[hhh, DiracTraceEvaluate -> True]
hhh3 = SUNTrace[hhh2]
% /. DiracTrace -> Tr
and finaly obtain expression with gamma matrices.
1/8 Tr[1] \[Delta]^(ab) tr(Overscript[\[Gamma], _]^5.\[Pi]f^b.Overscript[\[Gamma], _]^5.\[Pi]f^a)+g^2 N tr(Overscript[\[Gamma], _]^0.Overscript[\[Gamma], _]^\[Nu].Overscript[\[Gamma], _]^0.A^\[Nu].Overscript[\[Gamma], _]^\[Mu].A^\[Mu])+g m N tr(Overscript[\[Gamma], _]^\[Mu].A^\[Mu])+g m N tr(Overscript[\[Gamma], _]^0.Overscript[\[Gamma], _]^\[Nu].Overscript[\[Gamma], _]^0.A^\[Nu])+I g N tr(Overscript[\[Gamma], _]^0.(Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]).Overscript[\[Gamma], _]^0.Overscript[\[Gamma], _]^\[Mu].A^\[Mu])-I g N tr(Overscript[\[Gamma], _]^0.Overscript[\[Gamma], _]^\[Nu].Overscript[\[Gamma], _]^0.A^\[Nu].(Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]))+g N tr(\[Sigma].Overscript[\[Gamma], _]^\[Mu].A^\[Mu])+g N tr(Overscript[\[Gamma], _]^0.Overscript[\[Gamma], _]^\[Nu].Overscript[\[Gamma], _]^0.A^\[Nu].\[Sigma])-4 N Overscript[g, _]^(00) Overscript[p, _]^2-I N tr(\[Sigma].(Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]))+I N tr(Overscript[\[
Gamma], _]^0.(Overscript[\[Gamma], _]\[CenterDot]Overscript[p, _]).Overscript[\[Gamma], _]^0.\[Sigma])+8 N (Overscript[p, _]^0)^2+N Tr[\[Sigma].\[Sigma]]+4 m^2 N+8 m N \[Sigma]
What I am doing wrong?
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