Name: zhangyaworld (email_not_shown)
Date: 04/25/18-11:57:28 AM Z


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



This archive was generated by hypermail 2b29 : 11/20/18-10:40:01 PM Z CET