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Chin. Phys., 2003, Vol. 12(8): 841-845    DOI: 10.1088/1009-1963/12/8/004
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A set of Lie symmetrical non-Noether conserved quantity for the relativistic Hamiltonian systems

Cai Jian-Lea, Luo Shao-Kaib, Jia Li-Qunc
a Department of Physics, Hunan University, Changsha 410082, China; b Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China; Science College of Southern, Yangtze University, Wuxi 214063, China; Department of Physics, Hunan University, Changsha 410082, China; c Science College of Southern, Yangtze University, Wuxi 214063, China
Abstract  For the relativistic Hamiltonian system, a new type of Lie symmetrical non-Noether conserved quantities are given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, and introducing special infinitesimal transformations for q_s and p_s, we construct the determining equations of Lie symmetrical transformations of the system, which only depend on the canonical variables. A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example is given to illustrate the application of the results.
Keywords:  Hamiltonian system      Lie symmetry      non-Noether conserved quantity      relativity  
Received:  12 February 2003      Revised:  10 March 2003      Published:  16 March 2005
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  03.30.+p (Special relativity)  
  02.30.Hq (Ordinary differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 19972010), the Natural Science Foundation of Henan Province, China (Grant Nos 984053100 and 998040080), and the Scientific Research Foundation of the Education Bureau of Hunan

Cite this article: 

Cai Jian-Le, Luo Shao-Kai, Jia Li-Qun A set of Lie symmetrical non-Noether conserved quantity for the relativistic Hamiltonian systems 2003 Chin. Phys. 12 841

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