Generalized Weyl Quantization, Coherent State Quantization and Time in Quantum Mechanics

Daisy Romeo

Date of Award

2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Job A. Nable, PhD

Abstract

In this paper we consider two quantization techniques, the generalized Weyl quan- tization and coherent state quantization using the time of arrival functions as our object of quantization. Here time of arrival functions are expressed in different phase space variables, viz. R 2 , [−π, π) × ~Z and [−π, π) × R+ (forward cone). For each phase space there is a corresponding group of symmetry associated with it, and the groups are the Heisenberg group, S 1 × Z and E(2). In our quantization we also consider the different ordering schemes, both in generalized Weyl and coherent state quantizations. The computation of quantum expected values were done for both quantization methods. The novel results in this work are not only a contribution to the field of quantization but also to the field of phase space quantum mechanics. Moreover, many of the results involving coherent states are relevant to the parallel field of Signal Analysis.

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