Uncontracted Lorentz indices

[hongyi18]

I notice that in the development version, a free Lorentz index is always understood as an upper index, according to FeynCalc manual (development version) Is this also true in the stable version 9.3.1?

[vsht]

Yes, although it actually would matter only when breaking manifest Lorentz covariance via LorentzToCartesian. Do you have some particle case in mind?

[hongyi18]

Thanks for your answer. I am dealing with traces of gamma matrix products, with expressions like (you may directly copy and run in Mathematica)

SP[p1] = me^2;
SP[p2] = me^2;
SP[q] = 0;

\[Beta] := 1/(SP[p1-q]-me^2);
\[Delta] := 1/(SP[p2+q]-me^2);
Mat1 := \[Beta] GA[0] . (GS[p1-q]+me) . GA[5] + \[Delta] GA[5] . (GS[p2+q]+me) . GA[0];
Mat2 := \[Beta] GA[5] . (GS[p1-q]+me) . GA[0] + \[Delta] GA[0] . (GS[p2+q]+me) . GA[5];  (* \[Gamma]^0 Mat1^\[Dagger] \[Gamma]^0 *)

-DiracTrace[Mat1 . (GS[p1]+me) . Mat2 . (GS[p2]+me)] //DiracSimplify;
MSq = % //FCI

The final expression contains the temporal components of 4 momenta, and I just want to make sure that I understand these temporal components correctly.

[vsht]

That should be totally fine, all temporal indices are always upper indices. BTW, you can actually assign some values to the temporal components just the way you do it for scalar products,
e.g. via

TC[q] = q0
TC[p1] = p10

[hongyi18]

That's neat. Thanks!