Transient evolution of a photon gas in the nonlinear QED vacuum

Thermally induced vacuum polarization stemming from QED radiative corrections to the electromagnetic field equations is studied. The physical behavior of thermal radiation, in the nonlinear QED vacuum first described by Heisenberg and Euler, is a problem of some theoretical importance in view of its relation to the cosmic microwave background (CMB), early universe evolution, and Hawking-Unruh radiation. The questions of evolution toward equilibrium, stability, and invariance of thermal radiation under such conditions are of great interest. Our analysis presents novel aspects associated with photon-photon scattering in a photon gas in the framework of quantum kinetic theory. Within the context of the Euler-Heisenberg theory, we show that a homogeneous, isotropic photon gas with arbitrary spectral distribution function evolves toward an equilibrium state with a Bose-Einstein distribution. The transient evolution toward equilibrium of a gas of photons undergoing photon-photon scattering is studied in detail via the Boltzmann transport equation