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.
V2: 12 pages, minor improvements, references added; the version to appear in PLB
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