The braid group of a canonical Chern-Simons theory on a Riemann surface

Journal Article · Wed Jan 10 04:00:00 EST 1996 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1996.0001· OSTI ID:272737

Bergeron, M; Semenoff, G ^[1]

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1. Univ. of British Columbia, Vancouver, British Columbia (Canada)

The authors 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. They 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. They find an explicit solution of the Schrodinger equation. They 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. They find a fundamental constraint which relates the charges of the particles, q{sub i}, the coefficient k and the genus of the manifold, g: q{sub i}(Q+q{sub i}(g-1))/k is integer (where Q is the total charge). 18 refs., 3 figs.

• OSTI ID: 272737
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 245; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
ANYONS
GROUP THEORY
RIEMANN SPACE
SUPERCONDUCTIVITY