Geometric Quantum Mechanics in a Symplectic Framework: Metric-Affine Extensions and Deformed Quantum Dynamics
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Quantum Physics arXiv:2603.22354 (quant-ph) [Submitted on 22 Mar 2026] Title:Geometric Quantum Mechanics in a Symplectic Framework: Metric-Affine Extensions and Deformed Quantum Dynamics Authors:Hoshang Heydari View a PDF of the paper titled Geometric Quantum Mechanics in a Symplectic Framework: Metric-Affine Extensions and Deformed Quantum Dynamics, by Hoshang Heydari View PDF HTML (experimental) Abstract:We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard Kähler framework, we introduce an extension in which the symplectic structure is allowed to couple to a metric-affine background geometry, leading to a deformation of the Hamiltonian flow on the state space. We show that, under suitable conditions, the deformed structure remains symplectic and defines a well-posed Hamiltonian system. The formulation reduces to standard Schrödinger dynamics in the limit where the geometric deformation vanishes. Explicit analytical examples are constructed to illustrate the effect of the deformation. In particular, curvature-dependent deformations lead to a rescaling of Hamiltonian flows, while torsion-induced contributions produce direction-dependent corrections. In addition, geometric phases acquire corrections determined by the deformed symplectic structure. These results provide a mathematically consistent framework for exploring geometric modifications of quantum evolution induced by background curvature and affine structure. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2603.22354 [quant-ph] (or arXiv:2603.22354v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.22354 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hoshang Heydari [view email] [v1] Sun, 22 Mar 2026 12:47:16 UTC (10 KB) Full-text links: Access Paper: View a PDF of the paper titled Geometric Quantum Mechanics in a Symplectic Framework: Metric-Affine Extensions and Deformed Quantum Dynamics, by Hoshang HeydariView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: math math-ph math.MP 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?)