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

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.