Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-04-20
Nucl.Phys. B530 (1998) 349-400
Physics
High Energy Physics
High Energy Physics - Theory
48 pages, 3 figures, LaTeX2e; two remarks and a reference added, typos corrected; to appear in Nucl.Phys.B
Scientific paper
10.1016/S0550-3213(98)00572-0
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows that for the particular case of ISO(3) Chern-Simons theory the underlying symmetry is that of the quantum double D(SU(2)), based on the homogeneous part of the gauge group. This in contrast to the usual q-deformed gauge group itself, which occurs in the case of a homogeneous gauge group. Subsequently, we describe the structure of the quantum double of a continuous group and the classification of its unitary irreducible representations. The comultiplication and the R-element of the quantum double allow for a natural description of the fusion properties and the nonabelian braid statistics of the particles. These typically manifest themselves in generalised Aharonov-Bohm scattering processes, for which we compute the differential cross sections. Finally, we briefly describe the structure of D(SO(2,1)), the underlying quantum double symmetry of (2+1)-dimensional quantum gravity.
Bais Alexander F.
Müller Marius N.
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