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New Types of the Lie Symmetries and Conserved Quantities for a Relativistic Hamiltonian System |
| LUO Shao-Kai |
| Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003 |
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LUO Shao-Kai 2003 Chin. Phys. Lett. 20 597-599 |
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Abstract For a relativistic Hamiltonian system, two new types of the Lie symmetries and conservation laws are given under infinitesimal transformations of groups. On the basis of the theory of invariance of the relativistic Hamiltonian equations under infinitesimal transformations and introducing infinitesimal transformations for time t, generalized coordinates qs and generalized momentums ps, we obtain the determining equations, the structure equations and the conserved quantities of the Lie symmetries. Introducing infinitesimal transformation for generalized coordinates qs and generalized momentums ps, we construct the Lie symmetrical transformations of the system, which only depend on the canonical variables. A set of 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:
03.20.+i
03.30.+p
02.20.Sv
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Published: 01 May 2003
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