Symplectic quantum mechanics
type: Item
instance of: scholarly article
title: Symplectic quantum mechanics
zbMATH Open document ID: 1053.81061
author: Yanyan Li
published in: Annals of Physics
publication date: 2004-08-19T00:00:00Z
review text: The present paper addresses the problem of constructing unitary representations of the Galilei group and reinterpreting the Schrödinger equation in phase space, via symplectic geometry and the Weyl *-product. In this way, an alternative route to Wigner functions is established, not relying on the Liouville- von Neumann equation. Subsequently, applications to linear and nonlinear oscillators are presented, and the notion of coherent state discussed. The article is clearly written, and its methods and results may be usefully compared with other approaches in the same vein (see e.g., [\textit{S. T. Ali}, \textit{J.-P. Antoine}, \textit{J.-P. Gazeau} and \textit{U. A. Mueller}, Coherent states and their generalizations: A mathematical overview Rev. Math. Phys. 7 No. 7, 1013--1104 (1995; Zbl 0837.43014)], [\textit{S. T. Ali}, [Quantization techniques: a quick overview, in: Contemporary problems in mathematical physics (Cotonu 2001) 3--78 (River Edge, NJ, World Scientific) (2002; Zbl 1044.81068)] and references therein).
reviewed by: Mauro Spera
Mathematics Subject Classification ID: 81S30
Mathematics Subject Classification ID: 81S10
Mathematics Subject Classification ID: 81R20
Mathematics Subject Classification ID: 81R30
Mathematics Subject Classification ID: 70G45
zbMATH DE Number: 2092928
zbMATH Keywords: Weyl product
zbMATH Keywords: Galilei group
zbMATH Keywords: phase space
zbMATH Keywords: Wagner function
MaRDI profile type: Publication
full work available at URL: j.aop.2004.03.009
OpenAlex ID: W1971398751
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DOI: 10.1016/J.AOP.2004.03.009
description: scientific article; zbMATH DE number 2092928