Quantum Chern-Simons Vortices on a Sphere

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.

1+27 pages, LaTeX

References in corpus (3)

• Volume of Vortex Moduli Spaces
• Definition of Chern-Simons Terms in Thermal QED_3 Revisited
• Conservation Laws in a First Order Dynamical System of Vortices

Cited by in corpus (16)

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• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
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• Slow Schroedinger dynamics of gauged vortices
• Dynamics of CP^1 lumps on a cylinder
• Gauged vortices in a background
• Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
• Geometric quantization of the moduli space of the Self-duality equations on a Riemann surface
• Matrix supergroup Chern-Simons models for vortex-antivortex systems
• Vortex counting and the quantum Hall effect
• Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface
• A combinatorial formula for homogeneous moments
• Kähler quantization of vortex moduli
• The dimension of the Hilbert Space of Geometic quantization of vortices on a Riemann surface