Group-theoretic quantization of a particle on a torus in a constant magnetic field

Isham's group-theoretic quantization program is applied to a system consisting of a charged particle on a two-torus, with a constant magnetic field. The canonical group $\overline{\mathcal{G}}$ describing the symmetries of the system is a central extension of the universal cover of the symmetry group for the case without the magnetic field. The group $\overline{\mathcal{G}}$ is independent of the magnetic charge $n$, but its representations (and hence the quantizations of the system) depend on $n$.