中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3158-3162.doi: 10.1088/1674-1056/18/8/011

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Conformal invariance and conserved quantities of general holonomic systems in phase space

李元成1, 蔡建乐2, 夏丽莉3   

  1. (1)College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China; (2)College of Science, Hangzhou Normal University, Hangzhou 310018, China; (3)Department of Physics, Henan Institute of Education, Zhengzhou 450014, China
  • 收稿日期:2008-10-01 修回日期:2008-12-20 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    Project supported by the Key Disciplines' Building Foundation of Henan Institute of Education, the Natural Science Foundation of Education Bureau of Henan Province, China (Grant No 2009A140003).

Conformal invariance and conserved quantities of general holonomic systems in phase space

Xia Li-Li(夏丽莉)a)†, Cai Jian-Le(蔡建乐)b), and Li Yuan-Cheng(李元成)c)   

  1. a Department of Physics, Henan Institute of Education, Zhengzhou 450014, China; b College of Science, Hangzhou Normal University, Hangzhou 310018, China; c College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China
  • Received:2008-10-01 Revised:2008-12-20 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    Project supported by the Key Disciplines' Building Foundation of Henan Institute of Education, the Natural Science Foundation of Education Bureau of Henan Province, China (Grant No 2009A140003).

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摘要： This paper studies the conformal invariance and conserved quantities of general holonomic systems in phase space. The definition and the determining equation of conformal invariance for general holonomic systems in phase space are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.

Abstract: This paper studies the conformal invariance and conserved quantities of general holonomic systems in phase space. The definition and the determining equation of conformal invariance for general holonomic systems in phase space are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.

Key words: phase space, conformal invariance, conformal factor, conserved quantity

中图分类号:  (Momentum conservation)

  • 45.20.df
02.20.Qs (General properties, structure, and representation of Lie groups) 45.20.dh (Energy conservation)