Name: Peter Meinzinger (email_not_shown)
Date: 02/06/17-01:03:38 PM Z


Hi and thanks for the help,
i've got another, more general problem, regarding substitutions.
As for the code I had before, I now want to insert some relations, for example the Dirac equation and relations regarding the photon.
The simplifications, though, are not used.
See, for example, this code, the Dirac eq for the second spinor won't be used.

$BreitMaison = True
num1 := SpinorUBar[p3, ms].GA[6].(GS[q] + mt).GA[
   7].PolarizationVector[p2, \[Mu],
   Transversality -> True].(2*FV[q, \[Mu]] + 2*FV[p1, \[Mu]] +
    FV[p2, \[Mu]]).SpinorU[p1, mb]
num2 := SpinorUBar[p3, ms].gB.(GSD[q] + mt).GS[
   Polarization[p2]].(GS[q] + GS[p2] + mt).gA.SpinorU[p1, mb]

amp1 = num1*FAD[{q, mt}, {q + p1, mh}, {q + p1 + p2, mh}]
amp2 := num2*FAD[{q, mt}, {q + p2, mt}, {q + p2 + p1, mh}]
onshell = {SpinorUBar[p3, ms].DiracGamma[Momentum[p3, D]] ->
   ms*Spinor[Momentum[p3, D], ms, 1],
  DiracGamma[Momentum[p1, D]].Spinor[Momentum[p1, D], mb, 1] ->
   mb*Spinor[Momentum[p1, D], mb, 1],
  Pair[Momentum[p2, D], Momentum[p2, D]] -> 0,
  Pair[Momentum[p1, D],
    Momentum[Polarization[p2, I], D]] -> (mb^2 - ms^2)/2,
  Pair[Momentum[p3, D],
    Momentum[Polarization[p2, I], D]] -> (mb^2 - ms^2)/2,
  DiracGamma[Momentum[p1, D]].DiracGamma[6].Spinor[Momentum[p1, D],
     mb, 1] -> mb*DiracGamma[7].Spinor[Momentum[p1, D], mb, 1],
  DiracGamma[Momentum[p1, D]].DiracGamma[7].Spinor[Momentum[p1, D],
     mb, 1] -> mb*DiracGamma[6].Spinor[Momentum[p1, D], mb, 1],
  Pair[Momentum[p1, D], Momentum[p1, D]] -> mb^2,
  Pair[Momentum[p3, D], Momentum[p3, D]] -> ms^2,
  DiracGamma[Momentum[p1, D]].DiracGamma[5].Spinor[Momentum[p1, D],
     mb, 1] -> -mb*DiracGamma[5].Spinor[Momentum[p1, D], mb, 1],
  Momentum[-p1 - p2] -> Momentum[p3],
  DiracGamma[Momentum[Polarization[p2, I], D]].DiracGamma[
     Momentum[p2, D]] -> 0,
  Momentum[Polarization[p2, I], D].Momentum[p2, D] -> 0,
  DiracGamma[Momentum[p2, D]].DiracGamma[
     Momentum[Polarization[p2, I], D]] -> 0,
  Spinor[Momentum[p3, D], ms, 1].DiracGamma[Momentum[p3, D]] ->
   ms*Spinor[Momentum[p3, D], ms, 1],
  Pair[Momentum[p1],
    Momentum[Polarization[p2, I, Transversality -> True]]] -> p2epk}

res1 = -I/Pi^2*TID[amp1, q]
res2 = -I/Pi^2*TID[amp2, q]
res = res1 + res2 /. onshell
aux = FCDiracIsolate[res, Head -> StandardMatrixElement] //
    Expand2[#, {StandardMatrixElement, Pair}] & //
   ReplaceRepeated[#,
     a_Pair StandardMatrixElement[b_] :>
      StandardMatrixElement[a b]] & //
  Collect2[#, StandardMatrixElement] &
Cases2[aux,StandardMatrixElement]

Additionally, I sometimes get results, with a gamma matrix, but some code as superscript written, seems to be a bug somewhere, but I couldn't track it down to a function, I'll tell you if I find something more precise.
Cheers,
Peter



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