Eisenhart lift for higher derivative systems

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.

Original language	English
Pages (from-to)	86-90
Number of pages	5
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	765
DOIs	https://doi.org/10.1016/j.physletb.2016.11.059
Publication status	Published - 10 Feb 2017

Keywords

Eisenhart lift
Higher derivative mechanics

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.physletb.2016.11.059

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title = "Eisenhart lift for higher derivative systems",

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.",

keywords = "Eisenhart lift, Higher derivative mechanics",

author = "Anton Galajinsky and Ivan Masterov",

year = "2017",

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language = "English",

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journal = "Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics",

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AU - Masterov, Ivan

PY - 2017/2/10

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N2 - 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.

AB - 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.

KW - Eisenhart lift

KW - Higher derivative mechanics

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JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693