Name: Mikkel Bjoern (email_not_shown)
Date: 12/17/15-10:09:19 AM Z


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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