Article
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Quantization & the Koopman-von Neumann Formulation
Version 1
: Received: 25 November 2022 / Approved: 28 November 2022 / Online: 28 November 2022 (10:07:04 CET)
How to cite: Wallentin, F.N. Quantization & the Koopman-von Neumann Formulation. Preprints 2022, 2022110510. https://doi.org/10.20944/preprints202211.0510.v1 Wallentin, F.N. Quantization & the Koopman-von Neumann Formulation. Preprints 2022, 2022110510. https://doi.org/10.20944/preprints202211.0510.v1
Abstract
In a previous work by the author it was shown that the Koopman-von Neumann formulation of classical mechanics (KvN) exhibits quantum interference. As such it was there claimed that KvN ought to be considered as a proper quantum mechanical theory in a similar sense as ordinary non-relativistic quantum mechanics (OQM) is. In this article this claim is made manifest by showing that KvN and OQM can be taken as merely inequivalent representations resulting from one and the same quantization scheme. Of course, as the typical notion of quantization necessitates the canonical commutation relations (CCR) to hold, which they do not in KvN, the concept needs to be properly revised. To justify such a revision the typical reasons for necessitation the CCR, reductionism and quantization as 'turning brackets to commutators', are examined and found insufficient.
Keywords
Koopman-von Neumann formulation; canonical quantization; reductionism; Groenewold-van Hove theorem
Subject
Physical Sciences, Quantum Science and Technology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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