Euler-Heisenberg Lagrangian and photon circular polarization

Considering the effective Euler-Heisenberg Lagrangian, i.e., non-linear photon-photon interactions, we study the circular polarization of electromagnetic radiation based on the time-evolution of Stokes parameters. To the leading order, we solve the Quantum Boltzmann Equation for the density matrix describing an ensemble of photons in the space of energy-momentum and polarization states, and calculate the intensity of circular polarizations. Applying these results to a linear polarized thermal radiation, we calculate the circular polarization intensity, and discuss its possible relevance to the circular polarization intensity of the Cosmic Microwave Background radiation.