I am trying to evaluate the following lines
kinematicsreduce = {SP[SubPlus[k]] -> 0, SP[SubMinus[k]] -> 0,
SP[k12] -> 2 SP[p1, p2], SP[k34] -> 2 SP[p3, p4],
SP[k12, a_] -> SP[p1, a] + SP[p2, a],
SP[k34, a_] -> SP[p3, a] + SP[p4, a], SP[p1] -> 0, SP[p2] -> 0,
SP[p3] -> 0, SP[p4] -> 0, SP[SubPlus[k]] -> 0,
SP[SubMinus[k]] -> 0};
\[Nu]\[Nu]SMpart1 =
1/2 Tr[GS[p1].GA[\[Mu]].GS[p2].GA[\[Mu]p]] -
1/2 Tr[GS[p1].GA[\[Mu]].GS[p2].GA[\[Mu]p].GA[5]];
\[Nu]\[Nu]SMpart2 =
1/2 Tr[GS[p3].GA[\[Alpha]].GS[p4].GA[\[Alpha]p]] -
1/2 Tr[GS[p3].GA[\[Alpha]].GS[p4].GA[\[Alpha]p].GA[5]];
\[Nu]\[Nu]SMpart3Bsquared =
1/8 (Tr[GS[SubPlus[
k]].GA[\[Mu]].(GS[k12] - GS[k34]).GA[\[Alpha]].GS[SubMinus[
k]].GA[\[Alpha]p].(GS[k12] - GS[k34]).GA[\[Mu]p]] -
Tr[GS[SubPlus[k]].GA[\[Mu]].(GS[k12] - GS[k34]).GA[\[Alpha]].GS[
SubMinus[k]].GA[\[Alpha]p].(GS[k12] - GS[k34]).GA[\[Mu]p].GA[
5]]);
\[Nu]\[Nu]result2 =
Simplify[FCE[
Contract[\[Nu]\[Nu]SMpart1.\[Nu]\[Nu]SMpart2.\[Nu]\[Nu]\
SMpart3Bsquared ]] //. kinematicsreduce]
I have tried applying // Schouten but the Epsilons remain.
On my colleagues Mac the last line is rather pretty, only involving scalar products, on my PC there are a lot of Epsilon terms as well.
Best regards,
Mikkel
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