Lorentz-invariant photon number density

A Lorentz-invariant positive definite expression for photon number density is derived as the absolute square of the invariant scalar product of a polarization-sensitive position eigenvector and the photon wave function. It is found that this scalar product is independent of the form chosen for the wave function and that the normalized positive frequency vector potential–electric field pair is a convenient choice of wave function in the presence of matter. The number amplitude describing a localized state is a $\delta$ function at the instant at which localization and detection are seen as simultaneous.