An observable for the separation distance of two photons

TL;DR

This paper introduces a relativistic observable for the separation distance between two photons, enabling a meaningful localization measure, which is useful for analyzing photon systems in scattering experiments.

Contribution

It constructs a Hermitian separation observable for two photons, closely resembling the case of massive particles, which was previously not well-defined.

Findings

The separation probability density provides a meaningful localization picture.

The observable is tested on a model of two photons in scattering states.

The approach makes photon separation analysis more analogous to massive particle systems.

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.