Galilean One-Particle Kinematics from a Smooth Family of Reference States
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Quantum Physics arXiv:2604.09040 (quant-ph) [Submitted on 10 Apr 2026] Title:Galilean One-Particle Kinematics from a Smooth Family of Reference States Authors:Jianshuo Gao View a PDF of the paper titled Galilean One-Particle Kinematics from a Smooth Family of Reference States, by Jianshuo Gao View PDF HTML (experimental) Abstract:Giannelli and Chiribella derived an observable-generator duality for energy from a collision model of informational nonequilibrium. We study a continuous-variable version aimed at the Galilean one-particle sector. A smooth family of reference states around an isotropic equilibrium supplies time, translation, rotation, and boost directions. The local observable-generator correspondence is obtained by differentiating a smooth extension of the single-state duality map, and the norm-one property of localization is obtained from a fiducial focusing assumption together with covariance. Combined with the standard smearing form of covariant localization observables, this yields sharp localization. With local inertial composition, the spin-cover action of rotations, and a central boost-translation holonomy, every irreducible sector is unitarily equivalent to the Hilbert space L2(R3) tensored with a (2s+1)-dimensional spin space. In that representation translations are generated by the canonical momentum, the holonomy is a scalar mass m > 0, boosts at t = 0 are generated by m times the position observable, the Hamiltonian is the free-particle kinetic term plus a constant E0, and the total angular momentum is orbital plus spin. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.09040 [quant-ph] (or arXiv:2604.09040v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.09040 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jianshuo Gao [view email] [v1] Fri, 10 Apr 2026 07:01:03 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled Galilean One-Particle Kinematics from a Smooth Family of Reference States, by Jianshuo GaoView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?) 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?)