Polarization Vector for Quantum EM Field

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

I need to evaluate the following dot products

[tex]\vec{\epsilon}_{k,\,s}\cdot\vec{\epsilon}_{-k,\,s'} = ?[/tex]
[tex]\vec{\epsilon}_{k,\,s}^*\cdot\vec{\epsilon}_{-k,\,s'}^* = ?[/tex]​

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

Dr Transport

Science Advisor
Gold Member
Assume that the polarizations are along cartesian directions......

Meir Achuz

Science Advisor
Homework Helper
Gold Member
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.

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