Current-conserving relativistic linear response for collisional plasmas

We investigate the response of a relativistic plasma to electromagnetic fields in the framework of the Boltzmann equation incorporating a collision term in the relaxation rate approximation selected in a form assuring current conservation. We obtain an explicit solution for the linearized perturbation of the Fermi–Dirac equilibrium distribution in terms of the average relaxation rate κ. We study the resulting covariant, gauge invariant, and current conserving form of the polarization tensor in the ultrarelativistic and non-relativistic limits. We evaluate the susceptibility in the ultrarelativistic limit and explore their dependence on κ. Finally, we study the dispersion relations for the longitudinal and transverse poles of the propagator. We show that for κ>2ω_p, where ω_p is the plasma frequency, the plasma wave modes are overdamped. In the opposite case, κ≪ω_p, the propagating plasma modes are weakly damped.