| dc.identifier.uri | http://hdl.handle.net/1951/59574 | |
| dc.identifier.uri | http://hdl.handle.net/11401/71151 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.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. | |
| dcterms.available | 2013-05-22T17:34:07Z | |
| dcterms.available | 2015-04-24T14:46:11Z | |
| dcterms.contributor | Viro, Oleg | en_US |
| dcterms.contributor | Kirillov Jr.,
Alexander | en_US |
| dcterms.creator | Balsam, Benjamin | |
| dcterms.dateAccepted | 2013-05-22T17:34:07Z | |
| dcterms.dateAccepted | 2015-04-24T14:46:11Z | |
| dcterms.dateSubmitted | 2013-05-22T17:34:07Z | |
| dcterms.dateSubmitted | 2015-04-24T14:46:11Z | |
| dcterms.description | Department of Mathematics | en_US |
| dcterms.extent | 192 pg. | en_US |
| dcterms.format | Application/PDF | en_US |
| dcterms.format | Monograph | |
| dcterms.identifier | http://hdl.handle.net/1951/59574 | |
| dcterms.identifier | Balsam_grad.sunysb_0771E_11015 | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/71151 | |
| dcterms.issued | 2012-08-01 | |
| dcterms.language | en_US | |
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Previous issue date: 1 | en |
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Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Mathematics--Physics | |
| dcterms.subject | Quantum Algebra, Quantum Computing, Topological
Quantum Field Theory | |
| dcterms.title | Turaev-Viro theory as an extended
TQFT | |
| dcterms.type | Dissertation | |
