Quantum Chern-Simons Vortices on a Sphere

Details Quantum Chern-Simons Vortices on a Sphere Quantum Chern-Simons Vortices on a Sphere

2000-10-30

arxiv.org/abs/hep-th/0010277v2

J.Math.Phys. 42 (2001) 3445-3469

Physics

High Energy Physics

High Energy Physics - Theory

1+27 pages, LaTeX

Scientific paper

10.1063/1.1379315

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.

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