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Abstract: . We develop an approach to the classical limit of quantum theory using the mathematical framework of nonstandard analysis. In this framework infinitesimal quantities have a rigorous meaning, and the quantum mechanical parameter ¯ h can be chosen to be such an infinitesimal. We consider those bounded observables which are transformed continuously on the standard (non-infinitesimal) scale by the phase space translations. We show that, up to corrections of infinitesimally small norm, such... (Update)
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BibTeX entry: (Update)
R.F. Werner and M.P.H. Wolff: "Classical mechanics as quantum mechanics with infinitesimal ¯h", Phys.Lett.A 202(1995) 155--159 http://citeseer.ist.psu.edu/werner95classical.html More
@misc{ werner95classical,
author = "R. Werner and M. Wolff",
title = "Classical mechanics as quantum mechanics with infinitesimal ¯h",
text = "R.F. Werner and M.P.H. Wolff: Classical mechanics as quantum mechanics
with infinitesimal ¯h, Phys.Lett.A 202(1995) 155--159",
year = "1995",
url = "citeseer.ist.psu.edu/werner95classical.html" }
Citations (may not include all citations):26 Nonstandard methods in stochastic analysis and mathematical .. (context) - Albeverio, Fenstad et al. - 1986
12 Deformation quantization of Heisenberg manifolds (context) - Rieffel - 1989
8 The classical limit of quantum partition of functions (context) - Simon - 1980
6 North Holland (context) - Robinson, analysis - 1966
5 The classical limit for quantum mechanical correlation funct.. (context) - Hepp - 1974
4 Fedoriuk: Semi-classical approximation in quantum mechanics (context) - Maslov - 1981
4 Quantum statistical mechanics of general mean field systems (context) - Raggio, Werner - 1989
4 Quantum harmonic analysis on phase space (context) - Werner - 1984
3 Mean-field dynamical semigroups on C*-algebras (context) - Duffield, Werner - 1992
3 Wigner and Husimi functions in quantum mechanics (context) - Takahashi - 1986
2 the validity of the WKB approximation (context) - Burdick, Schmidt - 1994
2 A non-negative Wigner-type distribution (context) - Cartwright - 1976
2 Geometric dequantization and the correspondence problem (context) - Emch - 1983
2 The classical limit of quantum theory - Werner - 1994
2 An Invitation to Nonstandard Analysis (context) - Lindstrom - 1989
[Article contains additional citations not shown here]
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