Name: BWL Date: 06/22/20-11:50:06 AM Z


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!