Article
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Quantum Stability of Hamiltonian Evolution on a Finsler Manifold
Version 1
: Received: 21 May 2024 / Approved: 22 May 2024 / Online: 23 May 2024 (02:55:42 CEST)
How to cite: ELGRESSY, G.; HORWITZ, L. Quantum Stability of Hamiltonian Evolution on a Finsler Manifold. Preprints 2024, 2024051475. https://doi.org/10.20944/preprints202405.1475.v1 ELGRESSY, G.; HORWITZ, L. Quantum Stability of Hamiltonian Evolution on a Finsler Manifold. Preprints 2024, 2024051475. https://doi.org/10.20944/preprints202405.1475.v1
Abstract
This paper is a study of a generalization of the quantum Riemannian Hamiltonian evolution, previously
analyzed by us in our work [6], in the geometrization of quantum mechanical evolution in a Finsler geometry.
We find results with dynamical equations governing the evolution of the trajectories defined by the expectation values of position. The analysis appears to provide an underlying geometry described by a geodesic equation, with connection form with a second term which is an essentially quantum effect.
These dynamical equations provide a new geometric approach to the quantum evolution where we suggest a definition for "local instability" in the quantum theory.
Keywords
geometrization of quantum mechanical evolution; Finsler geometry; geodesic equation; quantum effect; local instability
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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