On geometric quantization of the Dirac magnetic monopole

TL;DR

This paper derives the spectrum of the Dirac magnetic monopole on a sphere using geometric quantization and explores its generalizations to coadjoint orbits of compact Lie groups.

Contribution

It provides a straightforward derivation of the monopole spectrum via geometric quantization and extends the discussion to more general coadjoint orbits.

Findings

Spectrum of Dirac magnetic monopole derived

Method based on geometric quantization and Frobenius reciprocity

Generalizations to coadjoint orbits discussed

Abstract

We give a simple derivation of the spectrum of the Dirac magnetic monopole on a unit sphere based on geometric quantization and the Frobenius reciprocity formula. We also briefly discuss the generalisations of Dirac magnetic monopole to any coadjoint orbit of a compact Lie group.