https://doi.org/10.1140/epjc/s10052-023-11684-8
Regular Article - Theoretical Physics
A new look at the Dirac quantization condition
1
Physics Department, CSU Fresno, 93740, Fresno, CA, USA
2
Department of Physics, University of Virginia, 22904-4714, Charlottesville, VA, USA
3
Physics Department, California State University Fresno, 93740, Fresno, CA, USA
4
Kavli Institute for Theoretical Physics, University of California Santa Barbara, 93106, Santa Barbara, CA, USA
Received:
6
December
2022
Accepted:
3
June
2023
Published online:
9
June
2023
The angular momentum of any quantum system should be 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 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.
© The Author(s) 2023
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