Name: Alaksiej Kacanovic Date: 03/07/17-04:20:48 PM Z
Subject: Dirac Trace Problem
To:
[feyncalc_at_HIDDEN-E-MAIL]
From: Alaksiej Kacanovic
<[noreply_at_HIDDEN-E-MAIL]>
Replyto:
[feyncalc_at_HIDDEN-E-MAIL]
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?