FeynCalc Mathematica : Polarization Vector Sum

[Hepth]

Does anyone here use Feyncalc? (Or have a better alternative).

I have terms that I need to simplify like :

(2 Pair[Momentum[p1], Momentum[PB]] Pair[Momentum[p2],
Momentum[Polarization[q, -I]]] Pair[Momentum[PB],
Momentum[Polarization[q, I]]])/(
Pair[Momentum[p1], Momentum[q]] Pair[Momentum[p2], Momentum[q]])

Which looks like :
$$\frac{(p1\cdot \varepsilon (q) )( p2\cdot \varepsilon^{*}(q))}{(p1 \cdot q)}$$

Everything is general 4-vectors, the polarizations also. Now this, by hand, is easily simplified by doing a polarization sum. The top is just -p1.p2, as the sum gives the negative metric tensor. I can't seem to do this in FeynCalc though. If you use "PolarizationSum[m,n]" itll just spit out the negative metric tensor, but the indices of p1,p2 and epsilon are all INTERNAL, so that [m,n], is actually something internal that I cannot specify.

Has anyone done something like this before? Or do you have an alternative program?

 

[Vailanor]

There is an alternative program called FormCalc which can be used to simplify expressions like this. It is a Mathematica-based package and uses the FeynCalc library, so you should be able to do the same simplification with it.

 

[oswaler]

Thank you for your question. I am familiar with FeynCalc and its use in simplifying complex expressions in quantum field theory calculations. In regards to your specific question, it seems that the issue lies in specifying the indices for the internal variables in the polarization sum. I would suggest reaching out to the FeynCalc community for assistance, as they may have encountered a similar problem and could provide a solution. Alternatively, there are other programs such as FORM and GiNaC that also have capabilities for simplifying expressions in quantum field theory. Ultimately, the best approach may depend on the specific problem you are trying to solve. I hope this helps and wish you success in your research.