Name: V. Shtabovenko Date: 10/19/17-04:47:15 PM Z
A small followup. While working on refactoring OneLoop
(which I hope to finish eventually *sigh*), I moved the
code responsible for wrapping spinor chains with StandardMatrixElement
head into a separate function.
The development version of FeynCalc now contains
ToStandardMatrixElement
which will give you standard matrix elements in the sense of Denner’s
famous paper on electroweak corrections (arXiv:0709.1075, Section 5).
AFAIK this was also the original reason why Rolf implemented this
functionality in OneLoop. Anyway, now one can do something like:
$BreitMaison = True;
num1 := SpinorUBar[p3, ms].GA[6].(GS[q] +
mt).GA[
7].PolarizationVector[
p2, \[Mu]].(2*FV[q, \[Mu]] +
2*FV[p1, \[Mu]] +
FV[p2, \[Mu]]).SpinorU[p1, mb] //
DiracSimplify
amp1 = num1*FAD[{q, mt}, {q + p1, mh}, {q + p1 + p2, mh}]
res1 = -I/Pi^2*TID[amp1, q, UsePaVeBasis -> True, ToPaVe ->
True];
res2 = ToStandardMatrixElement[res1]
var = Select[Variables[res2], (Head[#] ===
StandardMatrixElement) \&]
This might be useful for current/future collaborators of Denner and
Dittmaier ;)
Cheers,
Vladyslav
Am 13.02.2017 um 03:51 schrieb Vladyslav Shtabovenko:
> Hi,
>
> sorry for the late reply: I’m currently in the final stage of my
PhD, so
> I can answer at most once a week at this mailing list.
>
> Dirac equation is actually automatically applied by DiracSimplify.
Also
> in num2 you should use
> GS[Polarization[p2,Transversality->True] to have the
transversality
> condition. The kinematics
> like SP[p2,p2]=0 is usually specified before the calculation
(see
> examples bundled with FeynCalc).
>
> If you want to implement simplifications via replacement rules, you
need
> to first understand the difference
> between the FCI- and FCE-notation:
>
> https://github.com/FeynCalc/feyncalc/wiki/FAQ#fci_fce
>
> Then use StandardForm to see how Mathematica sees your expressions
and
> adjust the rules accordingly.
> For example, comparing
>
> Cases[res, DOT[___,
DiracGamma[Momentum[p1]],
Spinor[Momentum[p1], ___],
> ___], Infinity] // Union
> % // StandardForm
> onshell[[2]] // StandardForm
>
> it is quite easy to see why patterns do not match.
>
> Cheers,
> Vladyslav
>
> Am 06.02.2017 um 13:03 schrieb Peter Meinzinger:
>> 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]]