Polarization Vector for Quantum EM Field

[TriTertButoxy]

I'm doing some calculations and I've run into something rather strange.

I need to evaluate the following dot products

$$\vec{\epsilon}_{k,\,s}\cdot\vec{\epsilon}_{-k,\,s'} = ?$$
$$\vec{\epsilon}_{k,\,s}^*\cdot\vec{\epsilon}_{-k,\,s'}^* = ?$$​

where $\vec\epsilon_{k,\,s}$ is the normalized polarization vector for a single photon with momentum $k$, and spin $s$. Does anyone know where I can look for these identities?

 

[Dr Transport]

Assume that the polarizations are along cartesian directions...

 

[Meir Achuz]

If by "spin", you mean helicity, the e.e'=plus or minus 1, depending on the relative helicities. This works because the momenta are = and opposite.