On the notion of phase in mechanics

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Maurice de Gosson
Title: On the notion of phase in mechanics
Journal: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Year: 2004
Pagination: 7297-7314
ISSN: 0305-4470
Publisher: IOP PUBLISHING LTD
City: BRISTOL
URI/DOI: 10.1088/0305-4407/37/29/008
ISI number: 000223254200012
Organization: Blekinge Institute of Technology
Department: Department of Health, Science and Mathematics (Institutionen för hälso- och naturvetenskap)
Dept. of Health, Science and Mathematics S-371 79 Karlskrona
+46 455 38 50 00
http://www.bth.se/ihn/
Language: English
Abstract: The notion of phase plays an essential role in both semiclassical and quantum mechanics. But what is exactly a phase, and how does it change with time? It turns out that the most universal definition of a phase can be given in terms of Lagrangian manifolds by exploiting the properties of the Poincare-Cartan form. Such a phase is defined, not in configuration space, but rather in phase-space and is thus insensitive to the appearance of caustics. Surprisingly enough, this approach allows us to recover the Heisenberg-Weyl formalism without invoking commutation relations for observables.
Subject: Mathematics\Geometry
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