Dirac trace in D dimension with gamma_5

[phypar]

I know the trace $tr[\gamma_5 a\!\!\!/b\!\!\!/c\!\!\!/d\!\!\!/]$ in 4-dimensional space-time, how is the result of it in D dimension? Is it the same as in 4 dimension?

 

[andrien]

It is not easy to generalize γ₅ to higher dimension by demanding that it anticommutes with every γ_μ because this will lead directly to vanishing of the trace you have just written.Here we divide γ_μ into two parts which are for the original four dimensions and other components which are left.you can find more on this in following reference after 7.16