Eisenhart lift of Koopman-von Neumann mechanics

Abstract

The Eisenhart lift establishes a fascinating connection between non-relativistic and relativistic physics, providing a space-time geometric understanding of non-relativistic Newtonian mechanics. What is still little known, however, is the fact that there is a Hilbert space representation of classical mechanics (also called Koopman-von Neumann mechanics) that attempts to give classical mechanics the same mathematical structure that quantum mechanics has. In this article, we geometrize the Koopman-von Newmann (KvN) mechanics using the Eisenhart toolkit. We then use a geometric view of KvN mechanics to find transformations that relate the harmonic oscillator, linear potential, and free particle in the context of KvN mechanics.

arXiv comment32 pages, 1 figure, version to be published in Journal of Geometry and Physics

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Cited by in corpus (7)

• Schrödinger Symmetry in Gravitational Mini-Superspaces
• The wave operator representation of quantum and classical dynamics
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• More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques
• Conformally related vacuum gravitational waves, and their symmetries
• Lévy-Leblond Equation and Eisenhart-Duval lift in Koopman-von Neumann Mechanics
• Evading Quantum Mechanics à la Sudarshan: quantum-mechanics-free subsystem as a realization of Koopman-von Neumann mechanics