Quantum field theory at finite temperature: Renormalization and radiative corrections

We discuss radiative corrections and the renormalization prescription in finite-temperature quantum electrodynamics at the one-loop level. As an example we consider the Coulomb scattering of an electron on a heavy nucleus immersed in a heat bath of thermal photons. Temperature-dependent infrared divergences are shown to cancel in the corresponding cross section when allowing for soft, thermal bremsstrahlung as well as soft, thermal absorption processes. In the case of extreme-relativistic electrons, temperature-dependent mass singularities appear in the infrared-finite cross section. These singularities are shown to be cancelled by similar divergences in thermal emission and absorption processes. (orig.)