Hi Vladyslav,
I have two problem here.
====================First Problem====================
I've found a wired problem about the equivalence between GA[6] and (1+GA5)/2 (and GA[7]) within t'Hooft Scheme, i.e. with
$BreitMaison = True;
$Larin = False;
we have following results
1.for four gamma matrix, the results are the same:
A1 = DiracTrace[GAD[i1, i2].GA[6].GAD[i5, i6].GA[6],
DiracTraceEvaluate -> True];
A2 = DiracTrace[
GAD[i1, i2].((1 + GA[5])/2).GAD[i5, i6].((1 + GA[5])/2),
DiracTraceEvaluate -> True];
A1 - A2
0
2. for >= 6 gamma matrix, the terms involving Levi-Civita symbol are different:
A1 = DiracTrace[GAD[i1, i2, i3].GA[6].GAD[i5, i6, i7].GA[6],
DiracTraceEvaluate -> True];
A2 = DiracTrace[
GAD[i1, i2, i3].((1 + GA[5])/2).GAD[i5, i6, i7].((1 + GA[5])/2),
DiracTraceEvaluate -> True];
A1 - A2 // Simplify // Collect[#, Eps[___]] &
-2 I Eps[LorentzIndex[i2], LorentzIndex[i3], LorentzIndex[i6],
LorentzIndex[
i7]] (Pair[LorentzIndex[i1, -4 + D], LorentzIndex[i5, -4 + D]] -
Pair[LorentzIndex[i1, D], LorentzIndex[i5, D]]) (+...)
Tow common features, the first is this only happens for those involving two Gamma5 cases, and the second is that the results only differ in those involving Levi-Civita symbol.
(Actually what I want to calculate is a trace involving eight gamma matrix and two GA[6]).
So if I want to split the terms with/without involving Gamma5, what should I do?
Thanks!
====================Second Problem====================
The second problem is about a warning when I type
?$BreitMaison
The warning reads as
"The Breitenlohner-Maison gamma5 scheme is currently not supported by the Dirac algebra functions. Use Tracer if you need it."
So will it be problematic if I stick to use DiracTrace[x___]//TID[#, q, UsePaVeBasis -> True] & // ToPaVe[#, q] & to get the One-Loop integrals?
Thanks a lot!
Best wishes
Ya
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