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Dirac quantization of the rotator

L. Muenchow

Published Jan 1, 1990• 0 citations
OpenAlex

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Infinite-dimensional representations of the rotation group and Dirac monopole with an arbitrary magnetic charge

Alexander I. Nesterov, F. Aceves de la Cruz

Within the context of infinite-dimensional representations of the rotation group, the Dirac monopole problem is studied in details. We argue that an arbitrary magnetic charge is allowed, and the Dirac quantization condition can be replaced by a generalized quantization rule yielding a new quantum number, the so-called topological spin, which is related to the weight of the Dirac string. We find that the emerging difficulties in explanation of Aharonov-Bohm effect for an arbitrary Dirac string may be removed by introducing nonassociative path-dependent wave functions. The latter provides the absence of the AB effect for an arbitrary magnetic charge. Nevertheless, a singular string can be observed in the quantum-mechanical scattering process.

•Mar 4, 2005•0 citations
Within the context of infinite-dimensional representations of the rotation group, the Dirac monopole problem is studied in details. We argue that an arbitrary magnetic charge is allowed, and the Dirac quantization condition can be replaced by a generalized quantization rule yielding a new quantum number, the so-called topological spin, which is related to the weight of the Dirac string. We find that the emerging difficulties in explanation of Aharonov-Bohm effect for an arbitrary Dirac string may be removed by introducing nonassociative path-dependent wave functions. The latter provides the absence of the AB effect for an arbitrary magnetic charge. Nevertheless, a singular string can be observed in the quantum-mechanical scattering process.