# Bose-Einstein condensation of photons in a plasma

## TL;DR

This paper investigates the conditions and mechanisms for Bose-Einstein condensation of photons and plasmons in a plasma, highlighting the role of plasma-induced photon mass and interactions in enabling condensation.

## Contribution

It demonstrates that photon condensation can occur in unbounded plasmas due to an effective photon mass, and derives the interactions and excitations of the condensed photon and plasmon gases.

## Key findings

- Photon condensation is possible in unbounded plasma due to effective photon mass.
- Derived the dispersion relations for elementary excitations of the condensates.
- Analyzed the kinetics of photon condensation via inverse Compton scattering.

## Abstract

We study the Bose-Einstein condensation of photons in a plasma, where we include the cases of both transverse photons and plasmons. We consider four-wave mixing processes of photon and plasmon modes in a relativistic isotropic plasma to determine the coupling constant to lowest order. We further show that photon condensation is possible in an unbounded plasma because, in contrast with other optical media, plasmas introduce an effective photon mass. This guarantees the existence of a finite chemical potential and a critical temperature, which is calculated for both transverse photons and plasmons. By considering four-wave mixing processes, we derive the interactions between the photons in the condensate. We also study the elementary excitations (or Bogoliubov modes) of the condensed photon and plasmon gases, and determine the respective dispersion relations. Finally, we discuss the kinetics of photon condensation via inverse Compton scattering between the photons and the electrons in the plasma.