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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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