Hi,
see Sec 4.2 of https://arxiv.org/pdf/2001.04407.pdf
In short, FC will not evaluate D-dim traces with g^5 in the NDR scheme
because those are not algebraically well-defined quantities.
You can still do the calculation in D-dims and then apply your own
replacement rules to evaluate the traces separately
DiracTrace[GAD[tau, mu, ka, nu, rho, ka, si, tau, 5]] //
DiracSimplify // ReplaceAll[#, rule] & // EpsEvaluate
rule = FCI[
{DiracTrace[GAD[i1_, i2_, i3_, i4_, 5]] :> 4 I LC[i1, i2, i3, i4]}]
Cheers,
Vladyslav
Am 22.06.20 um 11:50 schrieb BWL:
> Hello authors!
>
> I got a problem when taking trace with gamma5 in D-dimension when there are other four gamma matrices:
>
> Tr[GAD[\[Mu], \[Nu], \[Lambda], \[Kappa], 5]] //FCE //StandardForm
>
> the result reads:
>
> DiracTrace[GAD[\[Mu]].GAD[\[Nu]].GAD[\[Lambda]].GAD[\[Kappa]].GA[5]]
>
> It's still keep the trace! And i wanna take the convention that the result in D-dimension is:
>
> Tr[1] I LC[\[Kappa], \[Lambda], \[Mu], \[Nu]]
>
> where Tr[1]=4 in my convention. Indeed if I use GA rather than GAD:
>
> Tr[GA[\[Mu], \[Nu], \[Lambda], \[Kappa], 5]] // FCE // StandardForm
>
> I obtain the result I want:
>
> 4 I LC[\[Kappa], \[Lambda], \[Mu], \[Nu]]
>
> But it's not so useful because in my definition the other gamma should live in D-dimension. So, how can I keep calculations in D-dimension while making sure the trace of GAD[5] with four other GAD[$\mu$] is the result I want?
>
> SJTU
> Best regards and many thanks!
>
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