Name: Vladyslav Shtabovenko (email_not_shown)
Date: 02/27/15-04:07:59 PM Z


Hi Kyrylo,

thanks for pointing this out and for testing the development version.
There was a problem with the Contract option for massive vector bosons,
such that the polarization sum didn't evaluate unless the option
Contract was set to False (default is True). This is now corrected

<https://github.com/FeynCalc/feyncalc/commit/d3783e2d5dc692386befd2b45a70d4d417c13ec7>

and DoPolarizationSums[tmp + 1, p] returns

3 - Pair[LorentzIndex[mu], LorentzIndex[nu]] + (
  Pair[LorentzIndex[mu], Momentum[p]] Pair[LorentzIndex[nu],
    Momentum[p]])/Pair[Momentum[p], Momentum[p]]

> 2) DoPolarizationSums[tmp+1,p,0] gives
> 4-g_{mu,nu}
> which is ok for tensor structure, but I expected 2 as a number.

The "4" comes from the fact that with this command you're replacing
Sum_{la=1,2} eps*^mu(p,la) eps^nu(p,la) by the so called
"pseudo-completeness relation" i.e.
Sum_{la=0,1,2,3} g_{lambda,lambda} eps*^mu(p,lambda) eps^nu(p,lambda)
which equals - g^{mu,nu}.But if there are no polarization vectors in the
expression, then "Sum_{la=0,1,2,3}" gives you 4.

Cheers,
Vladyslav

On 27/02/15 14:34, Kyrylo Bondarenko wrote:
> I found some strange behavior for DoPolarizationSums. Let
> tmp = Conjugate[PolarizationVector[p, mu]] PolarizationVector[p, nu]
>
> 1) DoPolarizationSums[tmp+1,p] gives
> 3+e_{mu} e_{nu}
> which is ok for number, but this command did nothing with polarizations.
>
> 2) DoPolarizationSums[tmp+1,p,0] gives
> 4-g_{mu,nu}
> which is ok for tensor structure, but I expected 2 as a number.
>
> 3) DoPolarizationSums[tmp+1,p,p] gives
> 2 + (-g_{mu,nu} + p_{mu}p_{nu}/p^2)
> which is ok for gluons, but it is not applicable for massive patricles because of 2, then 3.
>



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