An observable for the separation distance of two photons

Abstract

Motivated by an intention to apply partial wave analysis to systems containing photons, we construct eigenvectors of the distance of separation between two photons. A choice is made that makes the case of two photons most closely resemble the case of two massive particles. The treatment is relativistic. An Hermitian separation observable can then be defined, unlike a position operator for a single photon, which cannot be defined. We test these results on a model system of two photons meant to describe the initial or final state of a scattering experiment. We find that the separation probability density gives a meaningful picture of localization.