# FeynCalc Mathematica : Polarization Vector Sum

• Mathematica
• Hepth
It also has a built-in function for polarization sums.In summary, the conversation discusses the use of Feyncalc and asks for alternative programs to simplify expressions involving general 4-vectors and polarizations. The alternative program mentioned is FormCalc, which utilizes the FeynCalc library and has a built-in function for polarization sums.
Hepth
Gold Member
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?

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.

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.

## 1. What is FeynCalc Mathematica?

FeynCalc Mathematica is a powerful software package that allows users to perform calculations and simulations in theoretical physics, specifically in the field of quantum field theory.

## 2. How does FeynCalc Mathematica handle polarization vector sums?

FeynCalc Mathematica has built-in functions and tools that make it easy to handle polarization vector sums in calculations. These functions allow users to simplify the expressions and perform the necessary summations.

## 3. What is a polarization vector sum?

A polarization vector sum is a mathematical operation used in quantum field theory to calculate the scattering amplitude of particles. It involves summing over all possible polarizations of the particles involved in the scattering process.

## 4. Can FeynCalc Mathematica handle higher-order polarization vector sums?

Yes, FeynCalc Mathematica is capable of handling polarization vector sums of any order. This allows for more complex calculations and simulations in quantum field theory.

## 5. Is FeynCalc Mathematica user-friendly for beginners?

FeynCalc Mathematica can be a bit challenging for beginners as it requires a basic understanding of quantum field theory and familiarity with the Mathematica software. However, there are many resources available to help users learn how to use FeynCalc, such as tutorials and user guides.

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