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题名: Conformal killing tensors and covariant Hamiltonian dynamics
作者: Cariglia, M ;  Gibbons, GW ;  van Holten, JW ;  Horvathy, PA ;  Zhang, PM
刊名: JOURNAL OF MATHEMATICAL PHYSICS
出版日期: 2014
卷号: 55, 期号:12, 页码:122702
关键词: PERTURBED HYDROGEN-ATOM ;  DER-WAALS INTERACTION ;  HENON-HEILES SYSTEM ;  VARIABLE-SEPARATION ;  PAINLEVE PROPERTY ;  JACOBI EQUATION ;  QUANTUM DOTS ;  SYMMETRY ;  INTEGRALS ;  MOTION
学科分类: Physics
DOI: 10.1063/1.4902933
通讯作者: Cariglia, M (reprint author), Univ Fed Ouro Preto, DEFIS, Campus Morro Cruzeiro, BR-35400000 Ouro Preto, MG, Brazil.
部门归属: [Cariglia, M.] Univ Fed Ouro Preto, DEFIS, BR-35400000 Ouro Preto, MG, Brazil
英文摘要: A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Henon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six. (C) 2014 AIP Publishing LLC.
资助者: National Natural Science Foundation of China [11035006, 11175215]; Chinese Academy of Sciences [2010TIJ06]
收录类别: SCI
原文出处: 查看原文
语种: 英语
WOS记录号: WOS:000347168000028
Citation statistics: 
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/15555
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Recommended Citation:
Cariglia, M,Gibbons, GW,van Holten, JW,et al. Conformal killing tensors and covariant Hamiltonian dynamics[J]. JOURNAL OF MATHEMATICAL PHYSICS,2014,55(12):122702.
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