中国物理B ›› 2003, Vol. 12 ›› Issue (8): 841-845.doi: 10.1088/1009-1963/12/8/304

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A set of Lie symmetrical non-Noether conserved quantity for the relativistic Hamiltonian systems

蔡建乐1, 罗绍凯2, 贾利群3   

  1. (1)Department of Physics, Hunan University, Changsha 410082, China; (2)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; (3)Science College of Southern, Yangtze University, Wuxi 214063, China
  • 收稿日期:2003-02-12 修回日期:2003-03-10 出版日期:2003-08-16 发布日期:2005-03-16
  • 基金资助:
    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

A set of Lie symmetrical non-Noether conserved quantity for the relativistic Hamiltonian systems

Cai Jian-Le (罗绍凯)abc, Jia Li-Qun (贾利群)b, Luo Shao-Kai (蔡建乐)c    

  1. a Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China; b Science College of Southern, Yangtze University, Wuxi 214063, China; c Department of Physics, Hunan University, Changsha 410082, China
  • Received:2003-02-12 Revised:2003-03-10 Online:2003-08-16 Published:2005-03-16
  • Supported by:
    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

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摘要： 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.

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.

Key words: relativity, Hamiltonian system, Lie symmetry, non-Noether conserved quantity

中图分类号:  (Lie algebras of Lie groups)

  • 02.20.Sv
03.30.+p (Special relativity) 02.30.Hq (Ordinary differential equations)