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Chin. Phys. B, 2011, Vol. 20(3): 030201    DOI: 10.1088/1674-1056/20/3/030201
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Conformal invariance and a kind of Hojman conserved quantity of the Nambu system

Li Yan(李燕),Fang Jian-Hui(方建会),and Zhang Ke-Jun(张克军)
College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China
Abstract  Conformal invariance and a kind of Hojman conserved quantity of the Nambu system under infinitesimal transformations are studied. The definition and the determining equation of conformal invariance of the system are presented. The necessary and sufficient condition under which the conformal invariance of the system would have Lie symmetry under infinitesimal transformations is derived. Then, the condition of existence and a kind of Hojman conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.
Keywords:  conformal invariance      Nambu system      Hojman conserved quantity  
Received:  30 August 2010      Revised:  26 September 2010      Accepted manuscript online: 
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  02.20.Qs (General properties, structure, and representation of Lie groups)  
  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
Fund: Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 09CX04018A).

Cite this article: 

Li Yan(李燕),Fang Jian-Hui(方建会),and Zhang Ke-Jun(张克军) Conformal invariance and a kind of Hojman conserved quantity of the Nambu system 2011 Chin. Phys. B 20 030201

[1] Noether A E 1918 Nachr. Akad. Math. 2 235
[2] Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[3] Mei F X 2000 Beijing Inst. Technol. 9 120
[4] Mei F X 2001 Chin. Phys. 10 177
[5] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
[6] Galiullin A S, Gafarov G G, Malaishka R P and Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: UFN) p183 (in Russian)
[7] Robert M L and Matthew P 2001 J. Geom. Phys. 39 276
[8] He G and Mei F X 2008 Chin. Phys. B 17 2764
[9] Cai J L 2008 Chin. Phys. Lett. 25 1523
[10] Liu C, Mei F X and Guo Y X 2008 Acta Phys. Sin. 57 6704 (in Chinese)
[11] Fu J L, Wang X J and Xie F P 2008 Chin. Phys. Lett. bf 25 2413
[12] Cai J L, Luo S K and Mei F X 2008 Chin. Phys. B 17 3170
[13] Liu C, Liu S X, Mei F X and Guo Y X 2009 Chin. Phys. B 18 856
[14] Chen X W, Zhao Y H and Liu C 2009 Acta Phys. Sin. bf 58 5150 (in Chinese)
[15] Cai J L 2010 Int. J. Theor. Phys. 49 201
[16] Nambu Y 1973 Phys. Rev. D 7 2405
[17] Mukunda N and Sudarshan E C G 1976 Phys. Rev. D 13 2846
[18] Ogawa T and Sagae T 2000 Int. J. Theor. Phys. 39 2875
[19] Zhang K, Wang C and Zhou L B 2008 Acta Phys. Sin. bf 57 6718 (in Chinese)
[20] Lin P, Fang J H and Pang T 2008 Chin. Phys. B 17 4361
[21] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) p38 (in Chinese)
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