Quantum Kinetic Theory for Quantum Electrodynamics

We derive a quantum kinetic theory for QED including both elastic and inelastic collisions with screening effect. By assuming parity invariance at the lowest order in $hbar$, we find the classical limit of the kinetic theory generalizes the well-known classical kinetic theory to massive case. The resulting classical kinetic theory simplifies when fermion bare mass is much greater than thermal mass. In this case only elastic collision is relevant and screening is only needed for Coulomb scattering. For a given solution to the classical kinetic theory, we find at $O(hbar)$ non-dynamical part of the quantum correction to Wigner functions for fermion and photon, which gives rise to spin polarization for fermion and photon respectively. Other contributions to spin polarizations from dynamical part of the correction to Wigner function are possible when parity violating sources are present.