Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems

doi:10.1088/1674-1056/21/9/094501

中国物理B ›› 2012, Vol. 21 ›› Issue (9): 94501-094501.doi: 10.1088/1674-1056/21/9/094501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems

陈蓉, 许学军

Department of Physics, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2011-12-14 修回日期:2012-05-31 出版日期:2012-08-01 发布日期:2012-08-01

Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems

Chen Rong (陈蓉), Xu Xue-Jun (许学军)

Department of Physics, Zhejiang Normal University, Jinhua 321004, China

Received:2011-12-14 Revised:2012-05-31 Online:2012-08-01 Published:2012-08-01
Contact: Xu Xue-Jun E-mail:xxj@zjnu.cn

摘要/Abstract

摘要： In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.

关键词: Hamilton system, conformal invariance, conformal factor, conserved quantity

Abstract: In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.

Key words: Hamilton system, conformal invariance, conformal factor, conserved quantity

中图分类号: (Symmetry and conservation laws)

11.30.-j

45.20.Jj (Lagrangian and Hamiltonian mechanics) 02.20.Sv (Lie algebras of Lie groups)

陈蓉, 许学军. Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems[J]. 中国物理B, 2012, 21(9): 94501-094501.

Chen Rong (陈蓉), Xu Xue-Jun (许学军). Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems[J]. Chin. Phys. B, 2012, 21(9): 94501-094501.

参考文献 20

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Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems

Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems

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