约束Hamilton系统的积分因子和守恒量及其在场论中的应用

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 38-48.

约束Hamilton系统的积分因子和守恒量及其在场论中的应用

周景润¹(),傅景礼^2,*()

¹ 绍兴职业技术学院理科教研室浙江绍兴 312000
² 浙江理工大数学物理研究所杭州 310018

收稿日期:2017-10-10 出版日期:2019-02-26 发布日期:2019-03-12
通讯作者: 傅景礼 E-mail:869569521@qq.com;sqfujignli@163.com
作者简介:周景润, E-mail:869569521@qq.com
基金资助:
国家自然科学基金(11472247);国家自然科学基金(12722287);国家自然科学基金(11872335);浙江省科技创新团队项目(2013TD18)

Integrating Factors and Conserved Quantities for Constrained Hamilton Systems and Its Applications in Field Theory

Jingrun Zhou¹(),Jingli Fu^2,*()

¹ Science and Research Department of Science, Shaoxing Vacational and Technical College, Zhejiang Shaoxing 312000
² Institute of Mathematical Physics, Zhejiang Sci-Tech University, Zhejiang Hangzhou 310018

Received:2017-10-10 Online:2019-02-26 Published:2019-03-12
Contact: Jingli Fu E-mail:869569521@qq.com;sqfujignli@163.com
Supported by:
国家自然科学基金(11472247);国家自然科学基金(12722287);国家自然科学基金(11872335);浙江省科技创新团队项目(2013TD18)

摘要/Abstract

摘要：

在约束Hamilton系统的研究中，场论系统一直是重要且难度大的一部分.近年来，场论系统已经成为一个热门的研究领域.论文基于积分因子方法给出了构造场论系统守恒量的一般性方法.首先，构造了约束Hamilton系统的广义Hamilton正则方程；其次，给出了场论系统积分因子的定义和守恒定理；然后，建立了场论系统的广义Killing方程，从而导出系统的积分因子和守恒量；最后，给出了几个场论中的例子以说明这种方法的可行性和有效性.显然，与Noether对称性理论和Lie对称性理论相比较，这种方法具有步骤清晰，计算简便，限制条件少等优点.

关键词: 场论系统, 约束Hamilton系统, 积分因子, 自对偶场

Abstract:

Field theory is the most important and difficult part in the study of constrained Hamiltonian systems. In recent years, it has became a hot research area. In this paper, a general method that to construct the conservation laws of field theory system based on the integral factor method is presented. Firstly, the general Hamilton canonical equation of constrained Hamiltonian system is structured. Secondly, the definition about integrating factors is given and the conservation theorem for constrained Hamiltonian systems is established. Thirdly, the general Killing equation of constrained Hamiltonian system is deduced, then the integrating factors of constrained Hamiltonian systems are obtained. Finally, two examples are used to demonstrate the effectiveness of this method. Obviously, compared with Noether symmetry method and Lie symmetry method, the integrating factor method of constrained Hamiltonian system has the advantages of clearing calculation step, lessening restrictive conditions and simplifying operation and so on.

Key words: Field theory system, Constrained Hamilton system, Integrating factor, Self couple field

中图分类号:

O369

周景润,傅景礼. 约束Hamilton系统的积分因子和守恒量及其在场论中的应用[J]. 数学物理学报, 2019, 39(1): 38-48.

Jingrun Zhou,Jingli Fu. Integrating Factors and Conserved Quantities for Constrained Hamilton Systems and Its Applications in Field Theory[J]. Acta mathematica scientia,Series A, 2019, 39(1): 38-48.

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