Name: Xiangpeng Wang Date: 08/21/19-12:04:03 PM Z


Hi,

I think there might be a bug about SetMandelstam in D Dimension.

In[5]:= $BreitMaison = True;

In[13]:= SetMandelstam[s, t, u, p1, p2, -k1, -k2, 0, 0, m, m];

In[17]:= Pair[Momentum[k1, -4 + D], Momentum[k1, -4 + D]]

Out[17]= m^2

Which should be 0.

In some gamma5 involved D-dimensional traces, there would lead wrong results:

In[16]:= test1 =
 DiracTrace[(m + DiracGamma[Momentum[k2, D], D]).DiracGamma[
      LorentzIndex[mu3, D],
      D].(-m + DiracGamma[Momentum[k1, D], D]).DiracGamma[
      5].(m + DiracGamma[Momentum[k1, D], D]).DiracGamma[
      LorentzIndex[mu1, D],
      D].(m + DiracGamma[Momentum[-k1 - k2, D], D]).DiracGamma[
      LorentzIndex[mu3, D],
      D].(-m + DiracGamma[Momentum[k2, D], D]).DiracGamma[5]] /.
   DiracTrace -> Tr /. D -> 4

Out[16]= 0

In[15]:= test2 =
 ChangeDimension[
   DiracTrace[(m + DiracGamma[Momentum[k2, D], D]).DiracGamma[
      LorentzIndex[mu3, D],
      D].(-m + DiracGamma[Momentum[k1, D], D]).DiracGamma[
      5].(m + DiracGamma[Momentum[k1, D], D]).DiracGamma[
      LorentzIndex[mu1, D],
      D].(m + DiracGamma[Momentum[-k1 - k2, D], D]).DiracGamma[
      LorentzIndex[mu3, D],
      D].(-m + DiracGamma[Momentum[k2, D], D]).DiracGamma[5]], 4] /.
  DiracTrace -> Tr

Out[15]= -32 m^2 (m^2-s) Overscript[k1, _]^mu1