Quantum Chern-Simons Vortices on a Sphere

TL;DR

This paper performs geometric quantisation of Chern-Simons vortices on a sphere, linking classical moduli space volume to quantum Hilbert space dimension and analyzing angular momentum, supporting the interpretation of solitons as interacting bosons.

Contribution

It introduces a geometric quantisation approach for Chern-Simons vortices on a sphere, connecting classical and quantum properties of the system.

Findings

Quantum Hilbert space dimension relates to moduli space volume.

Angular momenta are consistent between classical and quantum models.

Results support solitons as interacting bosonic particles.

Abstract

The quantisation of the reduced first-order dynamics of the nonrelativistic model for Chern-Simons vortices introduced by Manton is studied on a sphere of given radius. We perform geometric quantisation on the moduli space of static solutions, using a Kaehler polarisation, to construct the quantum Hilbert space. Its dimension is related to the volume of the moduli space in the usual classical limit. The angular momenta associated with the rotational SO(3) symmetry of the model are determined for both the classical and the quantum systems. The results obtained are consistent with the interpretation of the solitons in the model as interacting bosonic particles.