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28 January 2022
 
  » arxiv » hep-th/0503040

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Infinite-dimensional representations of the rotation group and Dirac's monopole problem
Alexander I. Nesterov ; Fermin Aceves de la Cruz ;
Date 4 Mar 2005
Subject High Energy Physics - Theory; Mesoscopic Systems and Quantum Hall Effect; Mathematical Physics; Representation Theory | hep-th cond-mat.mes-hall math-ph math.MP math.RT quant-ph
AbstractWithin 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.
Source arXiv, hep-th/0503040
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