Kinetic theory of QED plasmas in a strong electromagnetic field II . The mean - field description

Starting from a general relativistic kinetic equation, a self-consistent mean-field equation for fermions is derived within a covariant density matrix approach of QED plasmas in strong external fields. A Schrödinger picture formulation on space-like hyperplanes is applied. The evolution of the distribution function is described by the one-particle gauge-invariant 4×4 Wigner matrix, which is decomposed in spinor space. A coupled system of equations for the corresponding Wigner components is obtained. The polarization current is expressed in terms of the Wigner function. Charge conservation is obeyed. In the quasi-classical limit for the Wigner components a relativistic Vlasov equation is obtained, which is presented in an invariant, i.e. hyperplane independent, form.