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Topological field theories and fractional statistics Bergeron, Mario
Abstract
We examine the problem of determining which representations of the braid group on a Riemann surface are carried by the wave function of a quantized Abelian Chern-Simons theory interacting with 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, the Riemann surface has arbitrary genus and the total matter charge is non-vanishing. We find an explicit solution of the SchrOdinger equation. We find that the wave functions carry a representation of the braid group as well as a projective representation of the discrete group of large gauge transformations. We find a fundamental constraint that relates the charges of the particles, q, the coefficient k and the genus of the manifold, g. We study the non-linear sigma model with a Chern-Simons term. We find the canonical structures of the model using Dirac bracket, accounting for the non-trivial constraints of the sigma-model. We show that solutions to the field equation are represented by solitons. We also recover braid group representations for the low energy limit of soliton exchange.
Item Metadata
Title |
Topological field theories and fractional statistics
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1993
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Description |
We examine the problem of determining which representations of the braid group on a Riemann surface are carried by the wave function of a quantized Abelian Chern-Simons theory interacting with 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, the Riemann surface has arbitrary genus and the total matter charge is non-vanishing. We find an explicit solution of the SchrOdinger equation. We find that the wave functions carry a representation of the braid group as well as a projective representation of the discrete group of large gauge transformations. We find a fundamental constraint that relates the charges of the particles, q, the coefficient k and the genus of the manifold, g. We study the non-linear sigma model with a Chern-Simons term. We find the canonical structures of the model using Dirac bracket, accounting for the non-trivial constraints of the sigma-model. We show that solutions to the field equation are represented by solitons. We also recover braid group representations for the low energy limit of soliton exchange.
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Extent |
4496856 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2008-09-17
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0085034
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1993-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.