INTRODUCTION TO THE FOCK QUANTIZATION OF THE MAXWELL FIELD

In this article we give an introduction to the Fock quantization of th e Maxwell field. At the classical level, we treat the theory in both t he covariant and canonical phase space formalisms. The approach is gen eral since we consider arbitrary (globally-hyperbolic) space-times. Th e Fock quantization is shown to be equivalent to the definition of a c omplex structure on the classical phase space. As examples, we conside r stationary space-times as well as ordinary Minkowski space-time. The account is pedagogical in spirit and is tailored to beginning graduat e students. The paper is self contained and is intended to fill an exi sting gap in the literature.