CLASSICAL MECHANICS AS QUANTUM-MECHANICS WITH INFINITESIMAL-H

Citation
Rf. Werner et Mph. Wolff, CLASSICAL MECHANICS AS QUANTUM-MECHANICS WITH INFINITESIMAL-H, Physics letters. A, 202(2-3), 1995, pp. 155-159
Citations number
23
Categorie Soggetti
Physics
Journal title
ISSN journal
03759601
Volume
202
Issue
2-3
Year of publication
1995
Pages
155 - 159
Database
ISI
SICI code
0375-9601(1995)202:2-3<155:CMAQWI>2.0.ZU;2-I
Abstract
We define the classical limit of quantum theory in the mathematical fr amework of nonstandard analysis, choosing h as an infinitesimal number . Up to corrections of infinitesimally small norm, bounded observables which change continuously on the standard (non-infinitesimal) phase s pace scale, are identified with functions on phase space. We discuss t he convergence of commutators to Poisson brackets, and the quantum tim e evolution to the classical one. These results are also shown for the classical limit of spin systems, by choosing the spin as an infinite half-integer.