A new look at the Dirac quantization condition

TL;DR

This paper critically examines the Dirac quantization condition for monopoles, revealing inconsistencies with pure Dirac monopoles and emphasizing the consistency of 't Hooft-Polyakov monopoles with angular momentum quantization and gauge invariance.

Contribution

It demonstrates that pure Dirac monopoles cannot satisfy angular momentum quantization due to gauge-variant angular momentum, unlike 't Hooft-Polyakov monopoles which are consistent.

Findings

Pure Dirac monopoles violate angular momentum quantization.

't Hooft-Polyakov monopoles are consistent with gauge-invariant angular momentum.

Field angular momentum from monopole-charge systems affects quantization.

Abstract

The angular momentum of any quantum system should be {\it unambiguously} quantized. We show that such a quantization fails for a pure Dirac monopole due to a previously overlooked field angular momentum from the monopole-electric charge system coming from the magnetic field of the Dirac string and the electric field of the charge. Applying the point-splitting method to the monopole-charge system yields a total angular momentum which obeys the standard angular momentum algebra, but which is gauge {\it variant}. In contrast it is possible to properly quantize the angular momentum of a topological 't Hooft-Polyakov monopole plus charge. This implies that pure Dirac monopoles are not viable -- only 't Hooft-Polyakov monopoles are theoretically consistent with angular momentum quantization and gauge invariance.