Comparison of classical and quantum theories of electromagnetism and the electrostatic field

A concise review of both classical and quantum theories of electromagnetism is given, with emphasis on the degree of equivalence between the theories. The significance of gauge constraints in quantum theory is discussed in detail, as is the role of the gauge in restoring Maxwell's theory in the classical limit. Results are presented which make explicit the effect of these gauge constraints for different formulations of the quantised theory. These results are applied to the problem of quantising the electrostatic field in a parallel plate capacitor. It is shown how the electrostatic field can be understood in terms of the average behaviour of a system of moving photons.