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Infinite-dimensional representations of the rotation group and Dirac's monopole problem

Alexander I. Nesterov·Fermin Aceves de la Cruz
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Abstract

Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are given by linear unbounded operators in infinite-dimensional topological spaces, supplied with a weak topology and associated weak convergence. 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.

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Alexander I. Nesterov, Fermin Aceves de la Cruz. 2005-06-30. Infinite-dimensional representations of the rotation group and Dirac's monopole problem. https://doi.org/10.1063/1.2830430

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