Euler-Heisenberg Lagrangian and photon circular polarization

Considering the effective Euler-Heisenberg Lagrangian, i.e., nonlinear 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.