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Title: Conformal killing tensors and covariant Hamiltonian dynamics

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 Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.
Authors:
 [1] ;  [2] ;  [3] ;  [3] ;  [4] ;  [5] ;  [6] ;  [7] ;  [6] ;  [7] ;  [7]
  1. DEFIS, Universidade Federal de Ouro Preto, Campus Morro do Cruzeiro, 35400-000 Ouro Preto, Minas Gerais (Brazil)
  2. Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge (United Kingdom)
  3. (France)
  4. NIKHEF, Amsterdam (Netherlands)
  5. (Netherlands)
  6. Laboratoire de Mathématiques et de Physique Théorique, Tours University, Tours (France)
  7. (China)
Publication Date:
OSTI Identifier:
22403071
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ELECTROMAGNETIC FIELDS; HAMILTONIANS; QUANTUM DOTS; TIME DEPENDENCE; VECTORS