Introduction to the Fock Quantization of the Maxwell Field

TL;DR

This paper introduces the Fock quantization of the Maxwell field, explaining the classical and quantum formalisms on arbitrary space-times, aimed at graduate students and filling a literature gap.

Contribution

It provides a comprehensive, pedagogical introduction to Fock quantization of the Maxwell field on general space-times, including classical formalisms and examples.

Findings

Equivalence of Fock quantization to complex structure on phase space

Application to stationary and Minkowski space-times

Pedagogical approach for graduate students

Abstract

In this article we give an introduction to the Fock quantization of the Maxwell field. At the classical level, we treat the theory in both the covariant and canonical phase space formalisms. The approach is general since we consider arbitrary (globally-hyperbolic) space-times. The Fock quantization is shown to be equivalent to the definition of a complex structure on the classical phase space. As examples, we consider stationary space-times as well as ordinary Minkowski space-time. The account is pedagogical in spirit and is tailored to beginning graduate students. The paper is selfcontained and is intended to fill an existing gap in the literature.