Name: Rolf Mertig Date: 04/07/06-01:26:34 PM Z
Hi,
first of all: you seem to have errors in your
input.
You write:
Lepton=FV[k1,mu]FV[k2,nu]+FV[k2,mu]VF[k1,nu]-SP[k1,k2]MT[mu,nu]
Quark=FV[p3,alhpa]FV[k,beta]+FV[k,alpha]VF[p3,beta]-SP[k,p3]MT[alpha,beta]
AA=GA[mu].(GS[p1+p3-k]+m).GS[alpha].(GS[p1]+m).GS[5].GS[S].GA[nu].(GS[k+p2-p3]+m).GA[beta].(GS[p2]-m)
However, I guess what you mean is:
Lepton = FV[k1, mu]*FV[k2, nu] + FV[k2,
mu]*FV[k1, nu] -
SP[k1, k2]*MT[mu, nu];
Quark = FV[p3, alpha]*FV[k, beta] + FV[k,
alpha]*FV[p3, beta] -
SP[k, p3]*MT[alpha, beta];
AA = GA[mu] . (GS[p1 + p3 - k] + m) . GA[alpha]
. (GS[p1] + m) .
GA[5] . GS[S] . GA[nu] . (GS[k + p2 -
p3] + m) . GA[beta] .
(GS[p2] - m);
r1=Calc[Lepton Quark AA];
r2=TR[r1]//Expand;
(* —————- *)
It is probably better for more complicated traces to
first use Calc or DiracSimplify and Contract before invoking TR.
Still, due to the Schouten identity the result may be
seemingly different.
You probably also should use energy-momentum conservation.
You have k1,k2,p3,k,p1,p3 and S as four-vectors.
They probably are not independent.
Rolf
Rolf