| A set of Lie symmetrical non－Noether conserved quantity for the relativistic Hamiltonian systems |
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| 引用本文： | 罗绍凯,贾利群,蔡建乐. A set of Lie symmetrical non－Noether conserved quantity for the relativistic Hamiltonian systems[J]. 中国物理, 2003, 12(8): 841-845. DOI: 10.1088/1009-1963/12/8/304 |
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| 作者姓名： | 罗绍凯 贾利群 蔡建乐 |
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| 作者单位： | (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 |
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| 基金项目： | 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 Province, China (Grant No 02C033). |
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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.
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| 关 键 词： | 相对论 哈密顿系统 李对称 非Noether保存量 动力学系统 |
| 收稿时间： | 2003-02-12 |
A set of Lie symmetrical non-Noether conserved quantity for the relativistic Hamiltonian systems |
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| Luo Shao-Kai,Jia Li-Qun and Cai Jian-Le. A set of Lie symmetrical non-Noether conserved quantity for the relativistic Hamiltonian systems[J]. Chinese Physics, 2003, 12(8): 841-845. DOI: 10.1088/1009-1963/12/8/304 |
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| Authors: | Luo Shao-Kai Jia Li-Qun Cai Jian-Le |
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| Affiliation: | 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 |
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| 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. |
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| Keywords: | relativity Hamiltonian system Lie symmetry non-Noether conserved quantity |
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