On Quantization, Contextuality & the Koopman-von Neumann Formulation

Fritiof Wallentin

doi:10.20944/preprints202302.0144.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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)

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.

Quantization; Koopman-von Neumann formulation; contextuality; classical statistical mechanics; Reductionism; the Classical limit

Physical Sciences, Mathematical Physics

Comment 1

Received: 14 April 2023
Commenter: Fritiof Wallentin
Commenter's Conflict of Interests: Author

Comment: Various notational errors and the linenumbering have been removed, and the abstract has been rewritten.

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On Quantization, Contextuality & the Koopman-von Neumann Formulation

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