Propagators of Charged Particles in External Active Media

Abstract

In this chapter, we give different representations of the charged particle propagators in an external active environment that will be needed for the analysis of quantum processes. The transformation from one representation to another are provided which can be useful from a methodological point of view. The exact propagator for an electron in a constant uniform magnetic field as the sum over Landau levels is obtained by the direct derivation by standard methods of quantum field theory from exact solutions of the Dirac equation in the magnetic field.