Energy–momentum conservation in classical electrodynamics and electrically bound quantum systems

Abstract

We call attention to the well-known fact that the electromagnetic (EM) field consists of bound and radiation components, and only their sum provides for the implementation of energy–momentum conservation for interacting classical charges. In this context, we then focus our attention on quantum systems of electrically bound charges, which do not radiate in the stationary energy states and thus their EM field comprises only the bound component. The non-applicability of Maxwell's equations to quantum mechanics does not permit, in general, ignoring the problem of recovering the energy–momentum conservation for such pure bound EM field systems, and we explore this problem within the Schrödinger–Dirac quantization scheme.