Inconsistent result for DiracTrace evaluations

[yaziddelenda-spec]

Hi,

I am evaluating Dirac traces in FeynCalc involving $\gamma^5$ and a massless momentum $p1$. Consider the two cases below:

<< FeynCalc`
SP[p1, p1] = 0;
T1 = I* DiracTrace[GS[p1] . GA[α] . GS[k1] . GA[β] . GS[p2] . GS[p1] . GA[5]]// DiracSimplify 
T2 = -I* DiracTrace[GS[p1] . GA[α] . GS[k1] . GA[β] . GS[p2] . GA[5] . GS[p1]]// DiracSimplify 

• In T2, FeynCalc simplifies the result to 0.
• In T1, I obtain a nonzero result proportional to an epsilon tensor.

Since GA[5] and GS[p1] anticommute, I expected both expressions to be equivalent and yield the same result, i.e. 0.

Could someone clarify why the results differ?

[vsht]

Could someone clarify why the results differ?

Because there's a thing called Schouten identity

https://feyncalc.github.io/FeynCalcBookDev/Extra/DiracTracesSchouten.html

[yaziddelenda-spec]

Thank you. Yes, the tensor expression simplifies to zero by Schouten identity.

Thanks for the reply