Name: Nicola Pessina Date: 05/13/03-09:39:56 AM Z

I think there is a bug in feyncalc…
See FILE A and FILE B (below).

The only difference between the two FILES is in the definition of the
matrix element “BB” .
The result should be the same in both cases because of trace ciclicity.
(the last term in FILE B is the first in FILE A: is the only difference)
But signs of “eps” is not the same in both cases for feyncalc……

Best regards,
             Nicola Pessina
                 Parma University, ITALY

FILE A:
-—————————————————
«HighEnergyPhysics`fc`

ScalarProduct[p,Dimension->D] = 0
ScalarProduct[l,Dimension->D] = 0
ScalarProduct[o,Dimension->D] = 0

BB = (DiracSlash[o, Dimension -> D]).
        DiracMatrix[rho, Dimension -> D].
      (DiracSlash[o, Dimension -> D]+ DiracSlash[l, Dimension -> D] ).
      DiracMatrix[mu, Dimension -> D].
      (1 - DiracMatrix[5]).
      DiracSlash[p, Dimension -> D].
      DiracMatrix[nu, Dimension -> D].
      (1 - DiracMatrix[5]).
      (DiracSlash[o, Dimension -> D]+ DiracSlash[l, Dimension -> D] ).
      DiracMatrix[rho, Dimension -> D]

trBB = Tr[BB,TraceOfOne->4]

contrazioneBB= Contract[trBB I LeviCivita[mu, nu, al, bet,Dimension->D]
      FourVector[p, al, Dimension -> D] (
      FourVector[o, bet, Dimension -> D] +
      FourVector[l, bet, Dimension -> D] -
      FourVector[p, bet, Dimension -> D] )]

contrazioneBB=contrazioneBB /. ScalarProduct[l,o,Dimension->D]
->ScalarProduct[l,o]
contrazioneBB=contrazioneBB /. ScalarProduct[l,p,Dimension->D]
->ScalarProduct[l,p]
contrazioneBB=contrazioneBB /. ScalarProduct[o,p,Dimension->D]
->ScalarProduct[o,p]

contrazioneBB=-contrazioneBB/4/2/ScalarProduct[l,o]/2/ScalarProduct[l,o]

Expand[contrazioneBB /. D -> 4 + 2 eps]

**********************************************************
File B:
-————————————————-
«HighEnergyPhysics`fc`

ScalarProduct[p,Dimension->D] = 0
ScalarProduct[l,Dimension->D] = 0
ScalarProduct[o,Dimension->D] = 0

BB = (DiracMatrix[rho, Dimension -> D]).(DiracSlash[o, Dimension -> D]).
        DiracMatrix[rho, Dimension -> D].
      (DiracSlash[o, Dimension -> D]+ DiracSlash[l, Dimension -> D]).
      DiracMatrix[mu, Dimension -> D].
      (1 - DiracMatrix[5]).
      DiracSlash[p, Dimension -> D].
      DiracMatrix[nu, Dimension -> D].
      (1 - DiracMatrix[5]).
      (DiracSlash[o, Dimension -> D]+ DiracSlash[l, Dimension -> D] )

trBB = Tr[BB,TraceOfOne->4]

contrazioneBB= Contract[trBB I LeviCivita[mu, nu, al, bet,Dimension->D]
      FourVector[p, al, Dimension -> D] (
      FourVector[o, bet, Dimension -> D] +
      FourVector[l, bet, Dimension -> D] -
      FourVector[p, bet, Dimension -> D] )]

contrazioneBB=contrazioneBB /. ScalarProduct[l,o,Dimension->D]
->ScalarProduct[l,o]
contrazioneBB=contrazioneBB /. ScalarProduct[l,p,Dimension->D]
->ScalarProduct[l,p]
contrazioneBB=contrazioneBB /. ScalarProduct[o,p,Dimension->D]
->ScalarProduct[o,p]

contrazioneBB=-contrazioneBB/4/2/ScalarProduct[l,o]/2/ScalarProduct[l,o]

Expand[contrazioneBB /. D -> 4 + 2 eps]

*******************************************************************