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The Braid Group of a Canonical Chern-Simons Theory on a Riemann Surface

✍ Scribed by Mario Bergeron; Gordon Semenoff

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
689 KB
Volume
245
Category
Article
ISSN
0003-4916

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✦ Synopsis

We examine the problem of determining which representations of the braid group on a Riemann surface and carried by the wave function of a quantized Abelian Chern Simons theory interacting with spinless non-dynamical matter. We generalize the quantization of Chern Simons theory to the case where the coefficient of the Chern Simons term, k, is rational (for a set of rational charges), the Riemann surface has arbitrary genus, and the total matter charge is non-vanishing. We find an explicit solution of the Schro dinger equation. We find that the wave functions carry a representation of the braid group as well as a dual projective representation of the discrete group of large gauge transformations. We find a fundamental constraint which relates the charges of the particles, q i , the coefficient k and the genus of the manifold, g : q i (Q+q i ( g&1))Γ‚k is integer (where Q is the total charge).

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