Article
Version 2
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On Quantization, Contextuality & the Koopman-von Neumann Formulation
Version 1
: Received: 6 February 2023 / Approved: 8 February 2023 / Online: 8 February 2023 (10:30:36 CET)
Version 2 : Received: 13 April 2023 / Approved: 14 April 2023 / Online: 14 April 2023 (02:41:46 CEST)
Version 2 : Received: 13 April 2023 / Approved: 14 April 2023 / Online: 14 April 2023 (02:41:46 CEST)
How to cite: Wallentin, F. On Quantization, Contextuality & the Koopman-von Neumann Formulation. Preprints 2023, 2023020144. https://doi.org/10.20944/preprints202302.0144.v2 Wallentin, F. On Quantization, Contextuality & the Koopman-von Neumann Formulation. Preprints 2023, 2023020144. https://doi.org/10.20944/preprints202302.0144.v2
Abstract
This article proposes a novel formulation of quantization, which considers the Koopman-von Neumann formulation (KvN) and ordinary non-relativistic quantum mechanics (OQM) as unitarily inequivalent representations of the same underlying structure. The approach is grounded in the notion that contextuality, rather than occurrence if Plank's constant, is the fundamental aspect of quantum mechanics. The motivation for this novel view arises from the limitations of traditional approaches to quantization, combined with previous research demonstrating contextuality in KvN. Using a representation-theoretic approach, both KvN and OQM are regarded as valid quantum theories, separated by a superselection rule.
Keywords
Quantization; Koopman-von Neumann formulation; contextuality; classical statistical mechanics; Reductionism; the Classical limit
Subject
Physical Sciences, Mathematical Physics
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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Commenter: Fritiof Wallentin
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