  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.
