Name: V. Shtabovenko (email_not_shown)
Date: 04/27/18-07:30:10 AM Z


Hi Ya,

sorry for the late reply. The difference is just a manifestation
of the Schouten's identity, on which you can find enough infos
in this forum or elsewhere

$BreitMaison = True;
A1 = DiracTrace[GAD[i1, i2, i3].GA[6].GAD[i5, i6, i7].GA[6],
    DiracTraceEvaluate -> True];
A2 = DiracTrace[
    GAD[i1, i2, i3].((1 + GA[5])/2).GAD[i5, i6, i7].((1 + GA[5])/2),
    DiracTraceEvaluate -> True];
diff = A1 - A2 // Simplify // Collect[#, Eps[___]] &

diff /. Pair[LorentzIndex[i_, -4 + D], LorentzIndex[j_, -4 + D]] :>
   (Pair[LorentzIndex[i, D], LorentzIndex[j, D]] -
     Pair[LorentzIndex[i], LorentzIndex[j]])
Schouten[%]

The tracing algorithms used in FeynCalc are not very advanced, so
results that differ by Schouten are unfortunately unavoidable. FORM is
much better in this sense, but it doesn't have a built in support for
the Dirac algebra in the BMHV scheme (although it should probably be
available via some external FORM packages).

Cheers,
Vladyslav

Am 25.04.2018 um 18:47 schrieb zhangyaworld:
> Hi Vladyslav,
>
> Oh, I've found that instead of using
>
> DiracTrace[GAD[i1, i2, i3].GA[6].GAD[i5, i6, i7].GA[6],DiracTraceEvaluate -> True];
>
> and
>
> DiracTrace[GAD[i1, i2, i3].((1 + GA[5])/2).GAD[i5, i6, i7].((1 + GA[5])/2), DiracTraceEvaluate -> True],
>
> which leads to two different results, the following two commands result into the same results.
>
> DiracTrace[GAD[i1, i2, i3].GA[6].GAD[i5, i6, i7].GA[6]// DotSimplify // DiracTrick // Simplify,DiracTraceEvaluate -> True];
>
> and
>
> DiracTrace[GAD[i1, i2, i3].((1 + GA[5])/2).GAD[i5, i6, i7].((1 + GA[5])/2)// DotSimplify // DiracTrick // Simplify, DiracTraceEvaluate -> True].
>
> But I'm still not sure how to get the Correct result (I don't want to check each calculation by hand).
>
> Thanks!
>
> Best,
> Ya
>



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