Field momentum and the reality of the Dirac String

TL;DR

This paper reveals that the Dirac string formulation of magnetic monopoles implies the existence of electromagnetic field momentum, challenging the physical reality of the Dirac monopole and its effectiveness as a topological monopole model.

Contribution

It demonstrates that the Dirac string monopole carries electromagnetic field momentum, questioning its status as a true monopole and its physical interpretation.

Findings

The monopole-charge system has an electromagnetic field momentum.

The Dirac string either carries hidden momentum or violates energy conservation.

Regulated Dirac monopoles are not true topological monopoles.

Abstract

It is well known that a magnetic monopole-electric charge system carries an angular momentum in its electromagnetic fields. Here we show that in the Dirac string formulation of magnetic charge the monopole-electric charge system also carries a momentum in its electromagnetic fields. This overlooked field momentum arises from the Coulomb electric field of the electric charge and the solenoidal magnetic field of the Dirac string. This implies that the monopole-charge system must either: (i) carry a ``hidden momentum" in the string, indicating that the string is real, or (ii) that the monopole-charge system violates the center-of-energy theorem. The overall conclusion is that the Dirac monopole with a {\it regulated} Dirac string is not a true monopole, and is not even a good effective description for topological monopoles ({\it e.g.} the 't Hooft-Polyakov monopole outside the core).