Photons in a Manifestly Lorentz-Covariant Theory

Abstract

Theoretical studies in near-field quantum electrodynamics are seldom carried out in the framework of the so-called covariant formulation, which is so important in relativistic quantum electrodynamics. In a sense this is very natural because near-field investigations up to this date have dealt exclusively with nonrelativistic problems. With this in mind it is understandable that the Coulomb gauge, and gauges related to this by a unitary transformation, have been in focus in classical and quantum near-field electrodynamics. We have seen in previous chapters of this book, however, that the longitudinal and scalar photons play an important conceptual role in the quantum mechanical (first-quantized) photon picture of near-field interactions. The purpose of this chapter is to give readers whose (main) background is in nonrelativistic (near-field) electrodynamics a brief introduction to the covariant formulation of classical and quantum electrodynamics in the free-field limit. Throughout the chapter near-field aspects will be emphasized when adequate.