Name: Carina Zanetti (email_not_shown)
Date: 08/23/11-11:53:21 PM Z


I have different results when I calculate some traces if I use Mathematica
5.2 or Mathematica 8.

For example when I calculate the following trace:

DS = DiracSigma[GA[k], GA[l]];
Simplify[TR[Contract[(DS.(GS[k - p] + m) + (GS[k - p] + m).DS).GA[a].(GS[k]
+ m).(GA[b].GS[y].GA[c].DS.GA[5])]]]

The output in Mathematica 5.2 is the following:

********************************Mathematica
5.2************************************************
\!\(16\ \[ImaginaryI]\ \((\(-3\)\ Eps[LorentzIndex[c], Momentum[
            k], Momentum[p], Momentum[y]]\ Pair[LorentzIndex[a], \
LorentzIndex[b]] +
            Eps[LorentzIndex[b], Momentum[k], Momentum[
              p], Momentum[y]]\ Pair[LorentzIndex[a], LorentzIndex[c]] + 6\
\
Eps[LorentzIndex[b], LorentzIndex[c],
            Momentum[k], Momentum[y]]\
              Pair[LorentzIndex[a], Momentum[k]] - 3\ Eps[LorentzIndex[b],
             LorentzIndex[c], Momentum[p], Momentum[y]]\ Pair[LorentzIndex[
              a], Momentum[k]] - 5\ Eps[LorentzIndex[b],
        LorentzIndex[c],
            Momentum[k], Momentum[y]]\
              Pair[LorentzIndex[a], Momentum[p]] - Eps[
            LorentzIndex[b], LorentzIndex[c], Momentum[k], Momentum[p]]\ \
Pair[LorentzIndex[a], Momentum[y]] - Eps[LorentzIndex[a], Momentum[
        k], Momentum[p], Momentum[y]]\ Pair[LorentzIndex[
            b], LorentzIndex[c]] - 3\ Eps[LorentzIndex[a], LorentzIndex[
            c], Momentum[p],
              Momentum[y]]\ Pair[LorentzIndex[b], Momentum[k]] + 5\ \
Eps[LorentzIndex[a], LorentzIndex[c], Momentum[k], Momentum[y]]\ Pair[
              LorentzIndex[b], Momentum[p]] +
                   Eps[LorentzIndex[
                    a], LorentzIndex[c], Momentum[k], Momentum[p]]\ \
Pair[LorentzIndex[
            b], Momentum[y]] + Eps[LorentzIndex[a], LorentzIndex[b], \
Momentum[p], Momentum[y]]\ Pair[LorentzIndex[c],
            Momentum[k]] - 3\ Eps[LorentzIndex[a], LorentzIndex[
              b], Momentum[k], Momentum[
              y]]\ Pair[LorentzIndex[c], Momentum[p]] + 3\ \
Eps[LorentzIndex[a], LorentzIndex[b],
        Momentum[k], Momentum[p]]\ Pair[LorentzIndex[c],
            Momentum[y]] + Eps[LorentzIndex[a], LorentzIndex[b],
               LorentzIndex[c], Momentum[y]]\ \((6\ m\^2 -
            3\ Pair[Momentum[k], Momentum[k]] + 5\ Pair[Momentum[
              k], Momentum[p]])\) + Eps[LorentzIndex[a], LorentzIndex[b],
            LorentzIndex[c], Momentum[
              p]]\ Pair[Momentum[k], Momentum[y]] - 3\ Eps[LorentzIndex[a],
\
LorentzIndex[b], LorentzIndex[c], Momentum[
            k]]\ Pair[Momentum[p], Momentum[y]])\)\)
********************************************************************************************************

And the output using Mathematica 8 is:

*************************Mathematica
8*************************************************************
16 I (-3 Eps[LorentzIndex[c], Momentum[k], Momentum[p],
     Momentum[y]] Pair[LorentzIndex[a], LorentzIndex[b]] +
   3 Eps[LorentzIndex[b], Momentum[k], Momentum[p], Momentum[y]] Pair[
     LorentzIndex[a], LorentzIndex[c]] +
   6 Eps[LorentzIndex[b], LorentzIndex[c], Momentum[k],
     Momentum[y]] Pair[LorentzIndex[a], Momentum[k]] -
   3 Eps[LorentzIndex[b], LorentzIndex[c], Momentum[p],
     Momentum[y]] Pair[LorentzIndex[a], Momentum[k]] -
   5 Eps[LorentzIndex[b], LorentzIndex[c], Momentum[k],
     Momentum[y]] Pair[LorentzIndex[a], Momentum[p]] -
   3 Eps[LorentzIndex[b], LorentzIndex[c], Momentum[k],
     Momentum[p]] Pair[LorentzIndex[a], Momentum[y]] -
   3 Eps[LorentzIndex[a], Momentum[k], Momentum[p], Momentum[y]] Pair[
     LorentzIndex[b], LorentzIndex[c]] -
   3 Eps[LorentzIndex[a], LorentzIndex[c], Momentum[p],
     Momentum[y]] Pair[LorentzIndex[b], Momentum[k]] +
   5 Eps[LorentzIndex[a], LorentzIndex[c], Momentum[k],
     Momentum[y]] Pair[LorentzIndex[b], Momentum[p]] +
   3 Eps[LorentzIndex[a], LorentzIndex[c], Momentum[k],
     Momentum[p]] Pair[LorentzIndex[b], Momentum[y]] +
   3 Eps[LorentzIndex[a], LorentzIndex[b], Momentum[p],
     Momentum[y]] Pair[LorentzIndex[c], Momentum[k]] -
   5 Eps[LorentzIndex[a], LorentzIndex[b], Momentum[k],
     Momentum[y]] Pair[LorentzIndex[c], Momentum[p]] +
   3 Eps[LorentzIndex[a], LorentzIndex[b], Momentum[k],
     Momentum[p]] Pair[LorentzIndex[c], Momentum[y]] +
   Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c],
     Momentum[y]] (6 m^2 - 3 Pair[Momentum[k], Momentum[k]] +
      5 Pair[Momentum[k], Momentum[p]]) +
   3 Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c],
     Momentum[p]] Pair[Momentum[k], Momentum[y]] -
   5 Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c],
     Momentum[k]] Pair[Momentum[p], Momentum[y]])
******************************************************************************************************



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