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arXiv · 2210.17522

A new look at the Dirac quantization condition

Michael Dunia·P. Q. Hung·Douglas Singleton
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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.

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Michael Dunia, P. Q. Hung, Douglas Singleton. 2022-09-12. A new look at the Dirac quantization condition. https://doi.org/10.1140/epjc/s10052-023-11684-8

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