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## 留言板

The Hamiltonian theory of Landau-Lifschitz equation and the gauge transformations

## The Hamiltonian theory of Landau-Lifschitz equation and the gauge transformations

He Jin-Chun, Chen Hua, Shi Li-Na, Huang Nian-Ning
• #### Abstract

The coordinate and spectral integral representations of Hamiltonian in isotropic LandauLifschitz equation are given by a standard procedure.But,the problem of deriving the corresponding conserved quantity to connect two kinds of integral mentioned above is still open.In this paper,using the gauge invariance properties,the compatibility pair of LL equation is transformed to the form-ikσ3+O(1) by choosing an app ropriate tr ansformation.Hence,the conserved quantities are obtained.The zeroth conserved qu antity,I0,is zero.The first one,I1,which has coordinate an d spe ctral integral representations,coincide with the two desired integral representations of the Hamiltonian.

• Funds:

#### Cited By

•  [1] Ding Guang-Tao. Effects of gauge transformations on symmetries of Birkhoffian system. Acta Physica Sinica, 2009, 58(11): 7431-7435. doi: 10.7498/aps.58.7431 [2] Mei Feng-Xiang. Lie symmetry and the conserved quantity of a generalized Hamiltonian system. Acta Physica Sinica, 2003, 52(5): 1048-1050. doi: 10.7498/aps.52.1048 [3] Jia Li-Qun, Zheng Shi-Wang. Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems. Acta Physica Sinica, 2007, 56(2): 661-665. doi: 10.7498/aps.56.661 [4] Xia Li-Li, Li Yuan-Cheng, Wang Xiao-Ming. Unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system. Acta Physica Sinica, 2010, 59(5): 2935-2938. doi: 10.7498/aps.59.2935 [5] Xia Li-Li, Li Yuan-Cheng, Wang Xiao-Ming, Liu Xiao-Wei. Lie-Mei symmetry and conserved quantities of Appell equation for a holonomic mechanical system. Acta Physica Sinica, 2010, 59(6): 3639-3642. doi: 10.7498/aps.59.3639 [6] Zheng Shi-Wang, Wang Jian-Bo, Chen Xiang-Wei, Li Yan-Min, Xie Jia-Fang. Lie symmetry and their conserved quantities of Tznoff equations for the vairable mass nonholonomic systems. Acta Physica Sinica, 2012, 61(11): 111101. doi: 10.7498/aps.61.111101 [7] Mei Feng-Xiang, Cai Jian-Le. Conformal invariance and conserved quantity of Lagrange systems under Lie point transformation. Acta Physica Sinica, 2008, 57(9): 5369-5373. doi: 10.7498/aps.57.5369 [8] Jia Li-Qun, Cui Jin-Chao, Zhang Yao-Yu, Luo Shao-Kai. Lie symmetry and conserved quantity of Appell equation for a Chetaev’s type constrained mechanical system. Acta Physica Sinica, 2009, 58(1): 16-21. doi: 10.7498/aps.58.16 [9] Xie Jia-Fang, Zheng Shi-Wang, Chen Xiang-Wei, Du Xue-Lian. Another kind of conserved quantity induced directly from Mei symmetry of Tzénoff equations for holonomic systems. Acta Physica Sinica, 2010, 59(8): 5209-5212. doi: 10.7498/aps.59.5209 [10] Xu Chao, Li Yuan-Cheng. Lie-Mei symmetry and conserved quantities of Nielsen equations for a singular nonholonomic system of Chetaev'type. Acta Physica Sinica, 2013, 62(12): 120201. doi: 10.7498/aps.62.120201
•  Citation:
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• Abstract views:  2548
• Cited By: 0
##### Publishing process
• Received Date:  21 November 2003
• Accepted Date:  09 October 2004
• Published Online:  10 May 2005

## The Hamiltonian theory of Landau-Lifschitz equation and the gauge transformations

• 1. (1)武汉大学数学与统计学院，武汉 430072; (2)武汉大学物理学院，武汉 430072

Abstract: The coordinate and spectral integral representations of Hamiltonian in isotropic LandauLifschitz equation are given by a standard procedure.But,the problem of deriving the corresponding conserved quantity to connect two kinds of integral mentioned above is still open.In this paper,using the gauge invariance properties,the compatibility pair of LL equation is transformed to the form-ikσ3+O(1) by choosing an app ropriate tr ansformation.Hence,the conserved quantities are obtained.The zeroth conserved qu antity,I0,is zero.The first one,I1,which has coordinate an d spe ctral integral representations,coincide with the two desired integral representations of the Hamiltonian.

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