Within the context of infinite-dimensional representations of the rotation group, the Dirac monopole problem is studied in detail. Irreducible infinite-dimensional representations, which have been 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.

Topics
Hall effect, Maxwell equations, Algebraic topology, General topology, Representation theory, Quantum field theory, Dirac quantization condition, Geometric phases, Hilbert space, Nuclear magnetic resonance
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© 2008 American Institute of Physics.
2008
American Institute of Physics
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