Eisenhart lift for higher derivative systems

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&#...

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Bibliographic Details
Main Authors:	Anton Galajinsky, Ivan Masterov
Format:	Article
Language:	English
Published:	Elsevier 2017-02-01
Series:	Physics Letters B
Subjects:	Higher derivative mechanics Eisenhart lift
Online Access:	http://www.sciencedirect.com/science/article/pii/S037026931630733X

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spelling	doaj-8d30e975a5b64a2b8ffa2b306fffc31f2020-11-24T20:49:06ZengElsevierPhysics Letters B0370-26931873-24452017-02-01765C869010.1016/j.physletb.2016.11.059Eisenhart lift for higher derivative systemsAnton GalajinskyIvan MasterovThe 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.http://www.sciencedirect.com/science/article/pii/S037026931630733XHigher derivative mechanicsEisenhart lift
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Anton Galajinsky Ivan Masterov
spellingShingle	Anton Galajinsky Ivan Masterov Eisenhart lift for higher derivative systems Physics Letters B Higher derivative mechanics Eisenhart lift
author_facet	Anton Galajinsky Ivan Masterov
author_sort	Anton Galajinsky
title	Eisenhart lift for higher derivative systems
title_short	Eisenhart lift for higher derivative systems
title_full	Eisenhart lift for higher derivative systems
title_fullStr	Eisenhart lift for higher derivative systems
title_full_unstemmed	Eisenhart lift for higher derivative systems
title_sort	eisenhart lift for higher derivative systems
publisher	Elsevier
series	Physics Letters B
issn	0370-2693 1873-2445
publishDate	2017-02-01
description	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.
topic	Higher derivative mechanics Eisenhart lift
url	http://www.sciencedirect.com/science/article/pii/S037026931630733X
work_keys_str_mv	AT antongalajinsky eisenhartliftforhigherderivativesystems AT ivanmasterov eisenhartliftforhigherderivativesystems
_version_	1716806760566620160

Eisenhart lift for higher derivative systems

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