Photon polarization vector (${ϵ}^{\mu }(k)$)

For a real on shell photon of null momentum $k$, a physical polarization satisfies $k\cdot ϵ=0$ and is defined modulo $ϵ\mapsto ϵ+\alpha k$. The two-dimensional quotient carries the two physical photon helicities. In a transverse gauge choose ${ϵ}^0=0$ and ${ϵ}^{\ast }\cdot ϵ=-1$. A Ward identity ensures that replacing an external polarization by its momentum gives zero in the summed physical amplitude.