Magnetic moments in the Poynting theorem, Maxwell equations, Dirac equation, and QED

TL;DR

This paper extends classical and quantum electrodynamics frameworks to describe electron magnetic dipole interactions using an extended Poynting theorem and Maxwell equations, unifying different formulations.

Contribution

It introduces a novel extension of the Poynting theorem and Maxwell equations to account for magnetic dipole sources, linking classical and quantum descriptions.

Findings

Extended Poynting theorem describes magnetic dipole interactions.

Consistent results between classical and quantum formulations.

Interactions expressed solely in terms of electromagnetic fields.

Abstract

This paper examines the theory of electron magnetic dipole moment interactions with magnetic fields or other electrons in classical and quantum electrodynamics. We show that these interactions may be described by a version of the Poynting theorem that is extended to take into account energetics of the interaction of magnetic dipole moments with inhomogeneous magnetic fields. This extension of the Poynting theorem is linked to an extension of the Maxwell equations that takes into account magnetic dipole moment sources. We provide detailed descriptions of the interactions based on both the extended Poynting theorem and on conventional quantum electrodynamics expressed in terms of electromagnetic fields and show that these apparently different formulations can give consistent results. In both cases, we express the interactions in terms of electromagnetic fields only, without the use of potentials. The main focus is on magnetic dipole interactions, and magnetic monopole interactions are not considered.