Conformal invariance and a kind of Hojman conserved quantity of the Nambu system

doi:10.1088/1674-1056/20/3/030201

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 30201-030201.doi: 10.1088/1674-1056/20/3/030201

• GENERAL • 下一篇

Conformal invariance and a kind of Hojman conserved quantity of the Nambu system

李燕, 方建会, 张克军

College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China

收稿日期:2010-08-30 修回日期:2010-09-26 出版日期:2011-03-15 发布日期:2011-03-15
基金资助:
Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 09CX04018A).

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

Received:2010-08-30 Revised:2010-09-26 Online:2011-03-15 Published:2011-03-15
Supported by:
Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 09CX04018A).

摘要/Abstract

摘要： 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.

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.

Key words: conformal invariance, Nambu system, Hojman conserved quantity

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

02.20.Qs (General properties, structure, and representation of Lie groups) 45.20.Jj (Lagrangian and Hamiltonian mechanics)

李燕, 方建会, 张克军. Conformal invariance and a kind of Hojman conserved quantity of the Nambu system[J]. 中国物理B, 2011, 20(3): 30201-030201.

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[J]. Chin. Phys. B, 2011, 20(3): 30201-030201.

参考文献 21

[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)

Conformal invariance and a kind of Hojman conserved quantity of the Nambu system

Conformal invariance and a kind of Hojman conserved quantity of the Nambu system

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 21

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Ping Liu(刘萍), Bing Huang(黄兵), Bo Ren(任博), and Jian-Rong Yang(杨建荣). Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves[J]. 中国物理B, 2021, 30(8): 80203-080203.
[2]	刘萍, 程杰, 任博, 杨建荣. Bäcklund transformations, consistent Riccati expansion solvability, and soliton-cnoidal interaction wave solutions of Kadomtsev-Petviashvili equation[J]. 中国物理B, 2020, 29(2): 20201-020201.
[3]	夏丽莉, 戈新生, 陈立群. Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems[J]. 中国物理B, 2019, 28(3): 30201-030201.
[4]	王建勇, 唐晓艳, 梁祖峰. Constructing (2+1)-dimensional N=1 supersymmetric integrable systems from the Hirota formalism in the superspace[J]. 中国物理B, 2018, 27(4): 40203-040203.
[5]	吉飞宇, 张顺利. New variable separation solutions for the generalized nonlinear diffusion equations[J]. 中国物理B, 2016, 25(3): 30202-030202.
[6]	魏含玉, 夏铁成. A new six-component super soliton hierarchy and its self-consistent sources and conservation laws[J]. 中国物理B, 2016, 25(1): 10201-010201.
[7]	王新赠, 董焕河. Hamiltonian structure, Darboux transformation for a soliton hierarchy associated with Lie algebra so(4, C)[J]. 中国物理B, 2015, 24(8): 80201-080201.
[8]	王建勇, 唐晓艳, 梁祖峰, 楼森岳. Generalized symmetries of an N=1 supersymmetric Boiti–Leon–Manna–Pempinelli system[J]. 中国物理B, 2015, 24(5): 50202-050202.
[9]	张智勇, 陈玉福. Conservation laws of the generalized short pulse equation[J]. , 2015, 24(2): 20201-020201.
[10]	刘萍, 曾葆青, 杨建荣, 任博. Exact solutions and residual symmetries of the Ablowitz-Kaup-Newell-Segur system[J]. 中国物理B, 2015, 24(1): 10202-010202.
[11]	屈改珠, 张顺利, 李尧龙. Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension[J]. , 2014, 23(11): 110202-110202.
[12]	夏丽莉, 陈立群, 傅景礼, 吴旌贺. Symmetries and variational calculationof discrete Hamiltonian systems[J]. , 2014, 23(7): 70201-070201.
[13]	Vikas Kumar, R. K. Gupta, Ram Jiwari. Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion–advection equation with variable coefficients[J]. 中国物理B, 2014, 23(3): 30201-030201.
[14]	M. M. Khader, Sunil Kumar, S. Abbasbandy. New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology[J]. 中国物理B, 2013, 22(11): 110201-110201.
[15]	Lakhveer Kaur, R. K. Gupta. On certain new exact solutions of the Einstein equations for axisymmetric rotating fields[J]. 中国物理B, 2013, 22(10): 100203-100203.