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]
*******************************************************************
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