Type
Text
Type
Dissertation
Advisor
Viro, Oleg | Kirillov Jr., Alexander
Date
2012-08-01
Keywords
Quantum Algebra, Quantum Computing, Topological Quantum Field Theory | Mathematics--Physics
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71151
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
In recent years, the application of quantum groups to the study of low-dimensional topology has become an active topic of research. In three-dimensions, these yield the well-known Reshetihkin-Turaev (RT) invariants, which are a mathematical formulation of Chern- Simons theory and Turaev-Viro (TV) theory, which is a convergent form of the Ponzano-Regge state sum formula from Quantum Gravity. Both RT and TV are more than invariants;they have a far richer structure known as a Topological Quantum Field Theory (TQFT). We describe Turaev-Viro theory as an extended (3-2-1)-TQFT and use this description to prove a theorem relating it to RT theory. Turaev-Viro theory has several equivalent descriptions. We examine Kitaev's toric code from quantum computation and the Levin- Wen model from condensed matter physics and show that these theories are extended TQFTs coinciding with TV theory. | 192 pages
Recommended Citation
Balsam, Benjamin, "Turaev-Viro theory as an extended
TQFT" (2012). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 358.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/358