Name: Alexander Artamonov (IHEP, Protvino, Russia) (email_not_shown)
Date: 10/08/04-05:16:18 PM Z

Dear Authors of the FeynCalc package,

Probably I've missed something but I wonder is it possible somehow to
produce a polarization sum from a polarization vector? I found the
FeynCalc package has the two functions: PolarizationVector and
PolarizationSum, but I'd like to get PolarizationSum[k,mu,nu] from
PolarizationVector[k,mu] and Conjugate[PolarizationVector[k,nu]].
Is it feasible?

Actually I want to calculate an amplitude having a polarization vector of
rho-meson. For the test I was trying to calculate the following simple
amplitude:

In[1]:= <<HighEnergyPhysics`fc`

In[2]:= a =
Spinor[p4,m4].DiracMatrix[5].Spinor[p2,m2].(Contract[FourVector[2*p3-2*p1,mu]
PolarizationVector[p1,mu]])
Out[2]= u[p4, m4] . ga[5] . u[p2, m2] . (2 p3.ep[p1])

In[3]:= ca=ComplexConjugate[a]
Out[3]= -2 u[p2, m2] . ga[5] . u[p4, m4] p3.ep(*)[p1]

In[4]:= FermionSpinSum[a ca]
Out[4]= -2 (tr[(gs[p2] + m2) ga[5] (gs[p4] + m4) ga[5]] 2
p3.ep[p1])p3.ep(*)[p1]

In[5]:= %/.DiracTrace->Tr
Out[5]= -2 (4 (m2 m4 - p2.p4) 2 p3.ep[p1]) p3.ep(*)[p1]

Now I'd like to make a spin sum over the rho-meson spin index but I did
not find anything on how to do this by FeynCalc. Of course this is easyly
done by "hands" but there may appear more complicated cases. Maybe there
exists more elegant way to calculate amplitudes having the polarization
vector? If so could you advise me please how to do that?

Best regards,
Alexander

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