Name: Vladyslav Shtabovenko (email_not_shown)
Date: 05/04/17-01:10:09 PM Z


Actually, the reverse also works, but it requires a DotSimplify:

DD = I*GS[p] - g*GA[\[Mu]].QuantumField[A, \[Mu]] - m -
    QuantumField[\[Sigma]] - I*GA[5]*SUNT[a].QuantumField[\[Pi]f, a];
DDh = (-I)*GA[0].GS[p].GA[0] -
    g*GA[0].GA[\[Nu]].GA[0].QuantumField[A, \[Nu]] - m -
    QuantumField[\[Sigma]] + I*GA[5].SUNT[b].QuantumField[\[Pi]f, b];
x1 = TR[SUNTrace[hhh]]
x2 = DiracTrace[DotSimplify[hhh], DiracTraceEvaluate -> True] //
   SUNTrace
Simplify[x1 - x2]

The reason why DiracTrace does not apply DotSimplify by itself,
is that traces often contain some recurring structures (like chiral
projectors), which DiracTrace/DiracTrick can recognize in order to speed
up the evaluation. However, DotSimpliy "destroys" these structures,
which is why I usually try to avoid it. Compare for example:

DiracTrace[GA[mu].(1 + GA[5]/2).GA[mu], DiracTraceEvaluate -> True]

and

DiracTrace[DotSimplify[GA[mu].(1 + GA[5]/2).GA[mu]],
  DiracTraceEvaluate -> True]
% // Contract

The former gets the final result right away, while the latter requires
an additional contract. Via the option FCVerbose->3 one can also see
explicitly, why is this so.

By the way, the current development version is actually much better
suited for this kind of calculations, than FeynCalc 9.2. This is because
in the developoment version we finally have support for Lorentz tensors
with spatial and temporal indices, so that things like

DiracSimplify[TGA[].GA[mu, nu].TGA[]]

(where TGA is shortcut for gamma^0) get properly simplified to

GA[mu].GA[nu] + 2 GA[nu].TGA[] MT[0, mu] - 2 GA[mu].TGA[] MT[0, nu]

Cheers,
Vladyslav

Am 03.05.2017 um 12:38 schrieb Rolf Mertig:
> Hi,
> I am using the latest development version of FeynCalc.
> Then:
> Needs["FeynCalc`"];
> DD = I*GS[p] - g*GA[\[Mu]] . QuantumField[A, \[Mu]] - m - QuantumField[\[Sigma]] -
> I*GA[5]*SUNT[a] . QuantumField[\[Pi]f, a];
> DDh = (-I)*GA[0] . GS[p] . GA[0] - g*GA[0] . GA[\[Nu]] . GA[0] . QuantumField[A, \[Nu]] - m -
> QuantumField[\[Sigma]] + I*GA[5] . SUNT[b] . QuantumField[\[Pi]f, b];
> hhh = DDh . DD;
> hhh2 = TR[SUNTrace[hhh]]
>
> works.
> Originally (last century) I assumed that color traces are always done before dirac traces. It definitely it easier. Maybe the current maintainer of the code base (Vladyslav) can comment if the reverse should and could also work. I am not so sure it is needed.
> Rolf
>



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