Symbol Correspondence for Euclidean Systems
Date of Award
2019
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Job A. Nable, PhD
Abstract
In this dissertation, we construct the star-product or ?-product of functions on the Euclidean motion group E(n), n = 2, 3 by way of the twisted convolution formulated on E(n). The construction is motivated by the theorem that connects the Weyl quanti- zation and the Wigner function given by hWσf|gi = (2π) −n/2 Z Rn Z Rn σ(x, ξ)WG(f, g)dxdξ, where Wσ is the Weyl quantization associated with σ in the Schwartz class, S (R n ), and WG(f, g) is the Wigner function of f, g ∈ S (R n ). The objects Wσ and WG(f, g) are constructed by means of the unitary irreducible representations of E(n). We will also show the properties of Wigner functions, as well as the ?-product of functions on E(n), and establish their relationship. The objects Wσ, WG and ? are three of the main objects of the formalism of quantum mechanics in phase space.
Recommended Citation
Natividad, Laarni, (2019). Symbol Correspondence for Euclidean Systems. Archīum.ATENEO.
https://archium.ateneo.edu/theses-dissertations/448
