Geometric Quantum Mechanics in a Symplectic Framework: Metric-Affine Extensions and Deformed Quantum Dynamics

Quantum Physics [Submitted on 22 Mar 2026] Geometric Quantum Mechanics in a Symplectic Framework: Metric-Affine Extensions and Deformed Quantum Dynamics Hoshang Heydari 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: 14 pages 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 Submission history From: Hoshang Heydari [view email] [v1] Sun, 22 Mar 2026 12:47:16 UTC (10 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)