Eisenhart lift of Koopman-von Neumann mechanics
arXiv:2207.05073 · doi:10.1016/j.geomphys.2022.104732
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.
32 pages, 1 figure, version to be published in Journal of Geometry and Physics
References in corpus (18)
- Quantum Decoherence
- Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
- Newtonian Gravity and the Bargmann Algebra
- (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
- Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
- The Eisenhart lift: a didactical introduction of modern geometrical concepts from Hamiltonian dynamics
- Eisenhart's theorem and the causal simplicity of Eisenhart's spacetime
- Classical aspects of lightlike dimensional reduction
- Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes
- Ricci-flat spacetimes admitting higher rank Killing tensors
- Eisenhart--Duval lift for minisuperspace quantum cosmology
- Self-dual metrics with maximally superintegrable geodesic flows
- Eisenhart Lift of --Dimensional Mechanics
- Gravitational Waves and Conformal Time Transformations
- Free fall in KvN mechanics and Einstein's principle of equivalence
- Implications of Kleinian relativity
- Time-dependent conformal transformations and the propagator for quadratic systems
- Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics
Cited by in corpus (6)
- Schrödinger Symmetry in Gravitational Mini-Superspaces
- The wave operator representation of quantum and classical dynamics
- Linearization of Newton's second law
- 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