Covariant linear response theory of relativistic QED plasmas

We start from the QED Lagrangian to describe a charged many-particle system coupled to the radiation field. A covariant density matrix approach to kinetic theory of QED plasmas, subjected to a strong external electro-magnetic field has recently been developed (Theor. Math. Phys. 131 (2002) 812; Theor. Math. Phys. 132 (2002) 1026). We use the hyperplane formalism in order to perform a manifest covariant quantization and to implement initial correlations to the solution of the Liouville-von Neumann equation. A perturbative expansion in orders of the fine structure constant for the correlation functions as well as the statistical operator is applied. The non-equilibrium state of the system is given within generalized linear response theory. Expressions for the susceptibility tensor, describing the plasma response, are calculated within different approximations, like the RPA approximation or considering collisions within the Born-approximation. In particular, the process of relativistic inverse bremsstrahlung in a plasma is discussed.