Eisenhart lift for higher derivative systems
arXiv:1611.04294 · doi:10.1016/j.physletb.2016.11.059
Abstract
The Eisenhart lift provides an elegant geometric description of a dynamical system of second order in terms of null geodesics of the Brinkmann-type metric. In this work, we attempt to generalize the Eisenhart method so as to encompass higher derivative models. The analysis relies upon Ostrogradsky's Hamiltonian. A consistent geometric description seems feasible only for a particular class of potentials. The scheme is exemplified by the Pais-Uhlenbeck oscillator.
arXiv commentV2: 12 pages, minor improvements, references added; the version to appear in PLB
References in corpus (19)
- Celestial Mechanics, Conformal Structures, and Gravitational Waves
- Benign vs malicious ghosts in higher-derivative theories
- Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator
- Conformal Properties of Chern-Simons Vortices in External Fields
- Conformal Properties of Chern-Simons Vortices in External Fields
- Eisenhart lifts and symmetries of time-dependent systems
- Some Spacetimes with Higher Rank Killing-Stackel Tensors
- Generalised Eisenhart lift of the Toda chain
- Killing tensors and canonical geometry
- Vanishing of the conformal anomaly for strings in a gravitational wave
- Curvatronics with bilayer graphene in an effective spacetime
- Higher rank Killing tensors and Calogero model
- Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
- Conformal Killing Tensors and covariant Hamiltonian Dynamics
- Ricci-flat spacetimes admitting higher rank Killing tensors
- Modified Hamiltonian formalism for higher-derivative theories
- Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors
- Self-dual metrics with maximally superintegrable geodesic flows
- A note on the Hamiltonian formalism for higher-derivative theories
Cited by in corpus (10)
- Schwarzian mechanics via nonlinear realizations
- Curvatronics with bilayer graphene in an effective spacetime
- General theory of Galilean gravity
- Some metrics admitting nonpolynomial first integrals of the geodesic equation
- Various disguises of the Pais-Uhlenbeck oscillator
- More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques
- Lifting the Eisenhart-Duval Lift to a Minimal Brane
- Higher time derivatives in the microcanonical ensemble describe dynamics of flux-coupled classical and quantum oscillators
- Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator
- The Bohlin variant of the Eisenhart lift