I have a contraction of three traces, for which the result depends on my naming of indices that are contracted out completely. I suspect the issue is with two-character issues, but I am not sure. And now, of course, I am unsure which result is right.
The two expressions are:
-- code ---------------------------------
Tmu1 = c1*Tr[GS[pm].GA[\[Mu]].GA[\[Nu]].GS[p].GA[\[Nu]m].GA[\[Mu]m]] +
c2*Tr[GS[pm].GA[\[Mu]].GA[\[Nu]].GS[p].GA[5].GA[\[Nu]m].GA[\[Mu]m]]
Tmu2 = c3*Tr[GS[l1].GA[\[Nu]].GS[l2].GA[\[Nu]m]] +
c4*Tr[GS[l1].GA[\[Nu]].GS[l2].GA[5].GA[\[Nu]m]]
Tmu3 = c5*Tr[GS[k1].GA[\[Mu]].GS[k2].GA[\[Mu]m]] +
c6*Tr[GS[k1].GA[\[Mu]].GS[k2].GA[5].GA[\[Mu]m]]
Simplify[FCE[Contract[Tmu1.Tmu2.Tmu3]]]
------------------------------------------
and the same, but where I exchange all "\[Nu]m" with "\[Alpha]" - producing EXTRA TERMS in the final trace (that do not simplify to zero, at least not according to Mathematica). Thus the code is
--- code -------------------------------
Tmu1 = c1*
Tr[GS[pm].GA[\[Mu]].GA[\[Nu]].GS[p].GA[\[Alpha]].GA[\[Mu]m]] +
c2*Tr[GS[pm].GA[\[Mu]].GA[\[Nu]].GS[p].GA[5].GA[\[Alpha]].GA[\[Mu]m]]
Tmu2 = c3*Tr[GS[l1].GA[\[Nu]].GS[l2].GA[\[Alpha]]] +
c4*Tr[GS[l1].GA[\[Nu]].GS[l2].GA[5].GA[\[Alpha]]]
Tmu3 = c5*Tr[GS[k1].GA[\[Mu]].GS[k2].GA[\[Mu]m]] +
c6*Tr[GS[k1].GA[\[Mu]].GS[k2].GA[5].GA[\[Mu]m]]
Simplify[FCE[Contract[Tmu1.Tmu2.Tmu3]]]
--------------------------------------------------
Since I suspceted the two-character index might be an issue I tried renaming all "\[Nu]m"'s to "\[Alpha]" and all "\[Mu]m"'s to "\[Beta]" - for which THE RESULT AGREES WITH THE ORIGINAL, that is, without the extra term.
Does anyone have an idea what is going on? I guess it is some kind of bug, since names of contracted indices should obviously now matter.
However I am new to Feyncal and could be doing something wrong.
Thank you!
Mikkel
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