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Quantization and Group Representations

Published online by Cambridge University Press:  20 November 2018

R. Cressman
R. Cressman*
Affiliation:
Memorial University of Newfoundland, Regional College at Corner Brook, Corner Brook, Newfoundland
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A quantization of a fixed classical mechanical system is firstly an association between quantum mechanical observables (preferably self-adjoint operators on Hilbert space) and classical mechanical observables (i.e. real-valued functions on phase space). Secondly, a quantization should permit an interpretation of the correspondence principle that ‘classical mechanics is the limit of quantum mechanics as Planck's constant approaches zero'. With these two underlying precepts, Section 2 states the four basic requirements, I to IV, of a quantization along with an additional requirement V that characterizes the subclass of special quantizations.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1264 - 1276
Copyright
Copyright © Canadian Mathematical Society 1977

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