On representations of the rotation group and magnetic monopoles

TL;DR

This paper extends the mathematical framework for magnetic monopoles by exploring unbounded infinite-dimensional representations of the rotation group, supporting a generalized Dirac quantization condition.

Contribution

It generalizes previous work by including unbounded representations, broadening the theoretical understanding of monopole quantization conditions.

Findings

Supports generalized Dirac quantization with unbounded representations

Extends previous bounded representation results

Provides a more comprehensive mathematical foundation for monopole theory

Abstract

Recently (Phys. Lett. A302 (2002) 253, hep-th/0208210; hep-th/0403146) employing bounded infinite-dimensional representations of the rotation group we have argued that one can obtain the consistent monopole theory with generalized Dirac quantization condition, $2\kappa\mu \in \mathbb Z$, where $\kappa$ is the weight of the Dirac string. Here we extend this proof to the unbounded infinite-dimensional representations.