consider Compton scattering amplitude:

$$M=-e^2 \bar{u}(p_3)[ \frac{\epsilon_{1\nu}\gamma^\nu(\gamma^{\alpha} p_{1\alpha}+\gamma^{\beta}p_{2\beta}+m)\gamma^\mu \epsilon_{1\mu}}{s-m^2}+\frac{\epsilon_{1\mu}\gamma^\mu(\gamma^{\alpha} p_{2\alpha}-\gamma^{\beta}p_{4\beta}+m)\gamma^\nu \epsilon_{1\nu}}{t-m^2}]u(p_2)$$ I know that if we have unpolarized photons we can sum over all polarizations and through ward identity simplify the traces (spurs). now my question is how will we proceed if there is light with an aribitrary polarization. or more specifically what properties should I use to simplify the expressions.note that I am "not" talking about linear polarizations specifically, hence the term "arbitrary polarization". Thank you.

p.s. can anyone tell me how to write slashed letters here.


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