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Chin. Phys. B, 2012, Vol. 21(9): 094501    DOI: 10.1088/1674-1056/21/9/094501
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

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

Chen Rong, Xu Xue-Jun
Department of Physics, Zhejiang Normal University, Jinhua 321004, China
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.
Keywords:  Hamilton system      conformal invariance      conformal factor      conserved quantity     
Received:  14 December 2011      Published:  01 August 2012
PACS:  11.30.-j (Symmetry and conservation laws)  
  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  02.20.Sv (Lie algebras of Lie groups)  
Corresponding Authors:  Xu Xue-Jun     E-mail:  xxj@zjnu.cn

Cite this article: 

Chen Rong, Xu Xue-Jun Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems 2012 Chin. Phys. B 21 094501

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