Stochastic phase space kinematics of the photon

Abstract

A stochastic phase space description of photon states is obtained by attaching to each circular polarization mode a probability amplitude at stochastic phase space points that are frontally localized. The ensuing formalism gives rise to a probability density at such points that transforms as a scalar under proper Lorentz transformations. There also exist conserved covariant currents associated with these probability densities. The wavefunctions corresponding to all extremal stochastic phase space representations can be embedded in a single Hilbert space, and give rise there to irreducible representations of the proper Poincaré group 𝒫↑+.