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

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

2005-03-04

arxiv.org/abs/hep-th/0503040v4

Physics

High Energy Physics

High Energy Physics - Theory

JHEP style. Extended version of hep-th/0403146. Revised version, title and some notations are changed. References and Appendix

Scientific paper

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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