{"id":{"repo_id":"ubc","oai_identifier":"oai:circle.library.ubc.ca:2429/2215"},"canonical_url":"https://search.dev.ndltd.org/etd/ubc/oai:circle.library.ubc.ca:2429/2215","repository":{"repo_id":"ubc","name":"University of British Columbia","base_url":"http://circle.library.ubc.ca/oai/request"},"display":{"title":"Topological field theories and fractional statistics","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Bergeron, Mario"],"institution":"University of British Columbia","degree_name":"Doctor of Philosophy - PhD","degree_level":"doctoral","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1993,"date_issued":"1993","date_published":"1993","updated_at":"2026-07-24T05:07:33Z","subjects":[],"languages":["eng"],"rights":["For non-commercial purposes only, such as research, private study and education. 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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."]},{"key":"dc:format","label":"Dc Format","values":["4496856","application/pdf"]},{"key":"dc:title","label":"Title","values":["Topological field theories and fractional statistics"]}]}],"canonical_facts":{"dc:creator":["Bergeron, Mario"],"dc:date":["1993"],"dc: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. 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