DEFORMATION QUANTIZATION AND THE FEDOSOV STAR-PRODUCT ON CONSTANT CURVATURE MANIFOLDS OFCODIMENSION ONE
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.
Advisor:George Sparling; Donna Naples; Gordon Belot; E. Ted Newman; Adam Leibovich
School:University of Pittsburgh
School Location:USA - Pennsylvania
Source Type:Master's Thesis
Date of Publication:06/26/2007