Considering the effective Euler-Heisenberg Lagrangian, i.e., non-linear photonphoton 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. : 73.50.Fq, 42.50.Xa, 98.70.Vc Introduction. Modern cosmological observations of the cosmic microwave background (CMB) radiation provide important evidences to understand our Universe. Cosmological informations encoded in the CMB radiation concerns not only temperature fluctuations and the spectrum of anisotropy pattern, but also the intensity and spectrum
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