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February 2001 Quantization of canonical isomorphisms and the semiclassical von Neumann theorem
Marcin MOSZYŃSKI
Hokkaido Math. J. 30(1): 25-64 (February 2001). DOI: 10.14492/hokmj/1350911922

Abstract

We prove the three mutually related theorems: the theorem on the quantizability of canonical isomorphisms, the theorem on the quantizability of classical canonical commutation relations and asemiclassical version of von Neumann's theorem. Although some similar results can be obtained on the basis of the deformation theory (e.g. [16], [15], [10] ) , here we present the proofs which involve only elementary methods and notions. Moreover, in our approach we can easily compute the quantum corrections. Our deformation quantizations (semiclassical algebras) are additionally equipped with the deformation involutions and we study here the algebras of entire functions and of polynomials, instead of frequently used algebras of $C^\infty$ observables.

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Marcin MOSZYŃSKI. "Quantization of canonical isomorphisms and the semiclassical von Neumann theorem." Hokkaido Math. J. 30 (1) 25 - 64, February 2001. https://doi.org/10.14492/hokmj/1350911922

Information

Published: February 2001
First available in Project Euclid: 22 October 2012

zbMATH: 1018.81028
MathSciNet: MR1814998
Digital Object Identifier: 10.14492/hokmj/1350911922

Subjects:
Primary: 81S05
Secondary: 81S99

Rights: Copyright © 2001 Hokkaido University, Department of Mathematics

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Vol.30 • No. 1 • February 2001
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