Tillman, Philip
(2007)
DEFORMATION QUANTIZATION AND THE FEDOSOV STAR-PRODUCT ON CONSTANT CURVATURE MANIFOLDS OFCODIMENSION ONE.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
In this thesis we construct the Fedosov quantization map on the phase-space of a single particle in the case of all finite-dimensional constant curvature manifolds embeddable in a flat space with codimension one. This set of spaces includes the two-sphere and de Sitter (dS)/anti-de Sitter (AdS) space-times. This quantization map was constructed by deformation quantization (DQ) techniques using, in particular, the algorithm provided by Fedosov.The purpose of this thesis was four-fold. One was to verify that this quantization procedure gave the same results as previous exact analyses of dS/AdS outside of DQ, i.e., standard dS and AdS quantum mechanics. Another was to verify that the formal series used in the conventional treatment converged by obtaining exact and nonperturbative results for these spaces. The third purpose was to illustrate the direct connection between the Fedosov algorithm, star-products, and the Hilbert space formulation of quantization. The fourth was to further develop and understand the technology of the Fedosov algorithm in the case of cotangent bundles, i.e., phase-space.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
26 June 2007 |
| Date Type: |
Completion |
| Defense Date: |
15 March 2007 |
| Approval Date: |
26 June 2007 |
| Submission Date: |
27 March 2007 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Physics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
deformation quantization; star-products |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-03272007-173751/, etd-03272007-173751 |
| Date Deposited: |
10 Nov 2011 19:33 |
| Last Modified: |
15 Nov 2016 13:37 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/6604 |
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