Eisenhart lifts and symmetries of time-dependent systems

doi:10.1016/j.aop.2016.07.033

	Eisenhart lifts and symmetries of time-dependent systems
	Cariglia, M.1,2; Duval, C.3,4,5; Gibbons, G. W.6,7; Horvathy, P. A.7,8
刊名	ANNALS OF PHYSICS
	2016-10-01
卷号	373 页码:631-654
关键词	Caldirola-Kanai model Damped oscillator Bargmann space Eisenhart lift Hubble model Dmitriev-Zel'dovich equations
ISSN号	0003-4916
DOI	10.1016/j.aop.2016.07.033
英文摘要	Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with n degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann space-time in n + 2 dimensions, equipped with its covariantly constant null Killing vector field. Reparametrisation of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrodinger equation emerges naturally using the techniques of quantum field theory in curved space times, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaltre and Bianchi cosmologies and how it fits in with our previous discussion in the non relativistic limit. (C) 2016 Elsevier Inc. All rights reserved.
资助项目	Brazilian funding agency CNPQ[205029/2014-0] ; Chinese Academy of Sciences' Presidential International Fellowship[2010T1J06]
WOS关键词	DAMPED HARMONIC-OSCILLATOR ; KINEMATICAL INVARIANCE GROUP ; QUANTUM-MECHANICS ; WITTEN MODEL ; SPACETIMES ; COSMOLOGY ; GEODESICS ; CONSTANT ; GEOMETRY ; UNIVERSE
WOS研究方向	Physics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000387734500040
资助机构	Brazilian funding agency CNPQ ; Chinese Academy of Sciences' Presidential International Fellowship
内容类型	期刊论文
源URL	[http://119.78.100.186/handle/113462/43817]
专题	中国科学院近代物理研究所
通讯作者	Cariglia, M.
作者单位	1.Univ Fed Ouro Preto, DEFIS, Ouro Preto, MG, Brazil 2.Univ Camerino, Dipartimento Fis, I-62032 Camerino, Italy 3.Aix Marseille Univ, Ctr Phys Theor, Case 907, F-13288 Marseille, France 4.Univ Toulon & Var, Case 907, F-13288 Marseille, France 5.CNRS UMR 7332, Case 907, F-13288 Marseille, France 6.Univ Cambridge, DAMTP, Cambridge CB2 1TN, England 7.Univ Tours, Lab Math & Phys Theor, F-37041 Tours, France 8.Chinese Acad Sci, Inst Modern Phys, Lanzhou, Peoples R China
推荐引用方式 GB/T 7714	Cariglia, M.,Duval, C.,Gibbons, G. W.,et al. Eisenhart lifts and symmetries of time-dependent systems[J]. ANNALS OF PHYSICS,2016,373:631-654.
APA	Cariglia, M.,Duval, C.,Gibbons, G. W.,&Horvathy, P. A..(2016).Eisenhart lifts and symmetries of time-dependent systems.ANNALS OF PHYSICS,373,631-654.
MLA	Cariglia, M.,et al."Eisenhart lifts and symmetries of time-dependent systems".ANNALS OF PHYSICS 373(2016):631-654.