Name: V. Shtabovenko Date: 06/24/20-04:20:14 PM Z
There is no need to make it so complicated. You can just employ a
slightly more generic replacement rule
rule = {
DiracTrace[
DOT[DiracGamma[a_, D], DiracGamma[b_, D],
DiracGamma[c_, D],
DiracGamma[d_, D], DiracGamma[5]]] :> 4
I Eps[a, b, c, d],
DiracTrace[
DOT[DiracGamma[a_, D], DiracGamma[b_, D],
DiracGamma[c_, D],
DiracGamma[d_, D], DiracGamma[e_, D],
DiracGamma[f_, D],
DiracGamma[5]]] :> myChiralTrace6[a, b, c, d,
e, f]
}
ex = DiracTrace[
GAD[tau, mu, ka].GSD[p1].GAD[nu, rho, ka, si,
tau, 5].GSD[p2]] //
DiracSimplify // ReplaceAll[#, rule] & // EpsEvaluate
and so on for 8 or more matrices. It doesn’t matter whether those are
GADs or GSDs.
Cheers,
Vladyslav
Am 24.06.20 um 15:23 schrieb BWL:
> Thank you!
>
> The way you suggested partly solved my problem, but if I wanna take
trace with something mixing with GSD, the ReplaceAll then doesn’t work
well.
> I now treat my problem with some clumsy way and the steps are as
follows:
> first, I finish taking trace in D-dimension, and let the result
shown in StandardForm;
> then, I replace all Ds with 4s and thus bring DiracTrace with
GA[5] back to 4 dimension;
> finally, I simplify the results from the 2nd step with DiracSimplify
and obtain the final result I want.
>
> In my example, the prescription above works however of course it’s
an ugly way at the same time…
>
> Best regards!
> BWL
>