Name: V. Shtabovenko (email_not_shown)
Date: 10/21/17-06:14:39 PM Z


FYI, in FeynCalc 9.3 DiracSimplify will try to canonicalize indices in
spinor chains, so that one can get the most compact result easier:

res=DiracSimplify[
    1/(2 (ieps + SP[q, q]))
      SpinorUBar[p - q,
       m1].(-(1/2)
          I kappa (1/
           4 ((FV[p, b] + FV[p - q, b]) GA[
               a] + (FV[p, a] + FV[p - q, a]) GA[b]) -
          1/2 (-m1 + 1/2 (GS[p] + GS[p - q])) MT[a, b])).SpinorU[p,
       m1] SpinorUBar[p + q,
       m2].(-(1/2)
          I kappa (1/
           4 ((FV[p, d] + FV[p + q, d]) GA[
               c] + (FV[p, c] + FV[p + q, c]) GA[d]) -
          1/2 (-m2 + 1/2 (GS[p] + GS[p + q])) MT[c, d])).SpinorU[p,
       m2] (MT[a, d] MT[b, c] + MT[a, c] MT[b, d] -
       MT[a, b] MT[c, d])] // Contract

Or (if one wants to have nicer dummy indices)

FCCanonicalizeDummyIndices[res, LorentzIndexNames -> {mu, nu}]

Cheers,
Vladyslav

> Thank you very much!!!
> Now that I understood that the $MU[1]s are just dummy indeces I also found another solution that gets rid of them:
>
> ToExpression[StringReplace[ToString[Calc[M] // StandardForm], "$MU[1]" -> "a"]]
>
> Again, thanks for your quick reply!!!
>
> Andreas

> Hi,
> you can get a result without $MU's by doing:
>
> DiracEquation[
> DotExpand[
> DiracGammaExpand[
> Expand[Contract[DotExpand[Contract[MomentumCombine2[Contract[M]]]]]]]]]
>
> However, the result can be simplified by renaming
> the indices ( c <--> d ), as you would do by hand.
>
> That is what I have automatized (which was actually quite non-trivial, especially if there are higher tensors involced) in DiracSimplify (which is used in Calc), and the dummy indices generated are called $MU[...] .
>
> Regards,
>
> Rolf Mertig
> GluonVision GmbH
> Berlin, Germany
> Mathematica training & consulting

>
>
> Hello forum,
>
> I encountered some problems when contracting Lorentz indeces while having Dirac matrices and spinors in my amplitudes. Here is my program:
>
> Tau1[p_, q_, m_, a_, b_] := -I*kappa/2*(1/4*(GA[a]*(FV[p, b] + FV[q, b]) + GA[b]*(FV[p, a] + FV[q, a])) - 1/2*MT[a,b] *(1/2*(DiracSlash[p] + DiracSlash[q]) - m));
> P[a_, b_, c_, d_] := 1/2*(MT[a, c]MT[b, d] + MT[a, d]MT[b, c] - MT[a, b]MT[c, d]);
> iDF[q_, a_, b_, c_, d_] := I*P[a, b, c, d] / (ScalarProduct[q,q] + ieps);
> M = -I*SpinorUBar[p - q, m1].Tau1[p, p - q, m1, a, b] . SpinorU[p, m1] * iDF[q, a, b, c, d] * SpinorUBar[p+q,m2] . Tau1[p, p + q, m2, c, d] . SpinorU[p, m2]
>
> If I now enter Contract[M], some Lorentz indeces are not contracted. If I enter Calc[M] or DiracSimplify[M], Mathematica gives strange results involving gamma matrices with index $MU(1).
>
> Does anyone know why this problem shows up and how I can get around it???
>
> Thank you very much,
>
> Andreas Ross



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