| 约束Hamilton系统的Lie对称性及其在场论中的应用 |
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| 引用本文： | 周景润,傅景礼.约束Hamilton系统的Lie对称性及其在场论中的应用[J].应用数学和力学,2019,40(7):810-822. |
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| 作者姓名： | 周景润 傅景礼 |
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| 作者单位： | 1绍兴职业技术学院 理科教研室, 浙江 绍兴 312000;2浙江理工大学 数学物理研究所, 杭州 310018 |
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| 基金项目： | 国家自然科学基金(11272287；11872335；11472247);浙江省科技创新团队（2013TD18） |
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| 摘 要： | 研究了约束Hamilton系统的Lie对称性，得到了场论系统的守恒量.首先给出约束Hamilton系统的正则运动方程和固有约束方程；其次构建了约束Hamilton 系统的Lie对称性确定方程和结构方程；然后给出了约束Hamilton系统的Lie守恒定理和守恒量；最后研究了复标量场与Chern-Simons项耦合系统的Lie对称性和另外一个例子以说明此方法在场论中的应用.
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| 关 键 词： | Lie对称性 约束Hamilton系统 场论 守恒量 |
| 收稿时间： | 2018-08-07 |
Lie Symmetry of Constrained Hamiltonian Systems and Its Application in Field Theory |
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| Institution: | 1Science Teaching and Research Section, Shaoxing Vocational and Technical College,Shaoxing, Zhejiang 312000, P.R.China;2Institute of Mathematical Physics, Zhejiang Sci Tech University,Hangzhou 310018, P.R.China |
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| Abstract: | The Lie symmetry method was studied for constrained Hamiltonian systems, and the conservation laws of the field theory systems were obtained. Firstly, the generalized canonical equations for constrained Hamiltonian systems were derived. Secondly, the determining equations and structural equations about the Lie symmetry of the constrained Hamiltonian systems were deduced. Thirdly, the Lie theorems and the conserved quantities for constrained Hamiltonian systems were given. Finally, the Lie symmetry for the system of the complex scalar field coupled to the Chern-Simons term was discussed. Two examples in the field theory illustrate the validity of this method. |
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