Geometry of the isotropic oscillator driven by the conformal mode

Abstract

Geometrization of a Lagrangian conservative system typically amounts to reformulating its equations of motion as the geodesic equations in a properly chosen curved spacetime. The conventional methods include the Jacobi metric and the Eisenhart lift. In this work, a modification of the Eisenhart lift is proposed which describes the isotropic oscillator in arbitrary dimension driven by the one-dimensional conformal mode.

V3: 10 pages, presentation improved, the version to appear in Eur. Phys. J. C

References in corpus (1)

• Minimal realization of $\ell$-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation

Cited by in corpus (11)

• Cosmological aspects of the Eisenhart-Duval lift
• Klein four-group and Darboux duality in conformal mechanics
• A variant of Schwarzian mechanics
• Gravitational Waves and Conformal Time Transformations
• Hidden symmetry and (super)conformal mechanics in a monopole background
• Time-dependent conformal transformations and the propagator for quadratic systems
• Dynamical realizations of the Lifshitz group
• Some metrics admitting nonpolynomial first integrals of the geodesic equation
• More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques
• The Bohlin variant of the Eisenhart lift
• Hidden symmetries and nonlinear (super)algebras