**Next message:**Francesco Saturnino: "saturnino@itp.unibe.ch Problem with Write2"**Previous message:**Vladyslav Shtabovenko: "Re: bug report"**Maybe in reply to:**Andreas Ross: "Problem with Contraction and Spinors"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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
*

**Next message:**Francesco Saturnino: "saturnino@itp.unibe.ch Problem with Write2"**Previous message:**Vladyslav Shtabovenko: "Re: bug report"**Maybe in reply to:**Andreas Ross: "Problem with Contraction and Spinors"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

*
This archive was generated by hypermail 2b29
: 11/22/17-04:40:02 AM Z CET
*