Uncertainty and Wigner negativity in Hilbert-space classical mechanics
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Quantum Physics arXiv:2602.10341 (quant-ph) [Submitted on 10 Feb 2026] Title:Uncertainty and Wigner negativity in Hilbert-space classical mechanics Authors:Mustafa Amin View a PDF of the paper titled Uncertainty and Wigner negativity in Hilbert-space classical mechanics, by Mustafa Amin View PDF HTML (experimental) Abstract:Classical mechanics, in the Koopman-von Neumann formulation, is described in Hilbert space. It is shown here that classical canonical transformations are generated by Hermitian operators that are in general noncommutative. This naturally brings about uncertainty relations inherent in classical mechanics, for example between position and the generator of space translations, between momentum and the generator of momentum translations, and between dynamical time and the Liouvillian, to name a few. Further, it is shown that the Wigner representation produces a quasi-probability distribution that can take on negative values. Thus, two of the hallmark features of quantum mechanics are reproduced, and become apparent, in a Hilbert-space formulation of classical mechanics. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Classical Physics (physics.class-ph) Cite as: arXiv:2602.10341 [quant-ph] (or arXiv:2602.10341v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.10341 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mustafa Amin [view email] [v1] Tue, 10 Feb 2026 22:24:45 UTC (31 KB) Full-text links: Access Paper: View a PDF of the paper titled Uncertainty and Wigner negativity in Hilbert-space classical mechanics, by Mustafa AminView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: math math-ph math.MP physics physics.class-ph References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)