Name: Vladyslav Shtabovenko (email_not_shown)
Date: 01/17/17-10:18:12 AM Z


Last month I finally modified the behavior of ComplexConjugate, such
that now dummy indices are renamed automatically

https://github.com/FeynCalc/feyncalc/commit/d7708286ef299bbb26ebed7d12f8737c3b02517a

c.f.

GA[mu, mu]
ComplexConjugate[GA[mu, mu]]

also

test = SpinorUBar[k2, m2].GA[mu].SpinorV[k1, m2] SpinorU[p1, m1].GA[
     mu].SpinorVBar[p2, m1] FeynAmpDenominator[PropagatorDenominator[s]]
ctest = ComplexConjugate[test]
(FermionSpinSum[test ctest] /. DiracTrace -> Tr) // Contract

One can turn that off via ComplexConjugate[exp,
FCRenameDummyIndices->False], of course. I hope that this
change would lower the number of wrong results obtained when squaring
the amplitude and forgetting to apply FCRenameDummyIndices.

The examples were also modified accordingly. Currently this change is
only in the development version, but will become standard in the next
stable release.

Cheers,
Vladyslav

> [quote]
> An example I have encountered is the following (e+ e- -> mu+ mu-):
> test = SpinorUBar[k2, m2].GA[mu].SpinorV[k1, m2] SpinorU[p1, m1].GA[
> mu].SpinorVBar[p2, m1] FeynAmpDenominator[
> PropagatorDenominator[s]]
> ctest = ComplexConjugate[test]
> FermionSpinSum[test ctest]
> [/quote]
>
> The problem here might come from (im not at a computer with FC) the fact that you have GA[mu] listed 4 times in the FSS. So when you have :
>
> (ub.GA[mu].u).(vb.GA[mu].v)
>
> and take the complex conjugate, it doesnt relabel the indices. I always do something like:
>
> AMP = (SpinorUBar[k2, m2].GA[mu].SpinorV[k1, m2]) (SpinorU[p1, m1].GA[
> mu].SpinorVBar[p2, m1]);
>
> AMPSQ = FermionSpinSum[Calc[AMP.ComplexConjugate[AMP/.{mu-> nu}]]]/.DiracTrace-> Tr
>
> As my standard squared amplitude.
>
> Also I use the "." a lot, and Calc[A.A*] before the FSS.



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