Topological field theories and fractional statistics

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.

Name thesis:degree_name

Doctor of Philosophy - PhD

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Physics

Grantor dc:publisher

University of British Columbia

Year dc:date

1993

Author dc:creator

• Bergeron, Mario

Statement dc: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.

Language dc:language

eng

Handle dc:identifier

http://hdl.handle.net/2429/2215

OAI identifier oai:identifier

oai:circle.library.ubc.ca:2429/2215