约束Hamilton系统的积分因子和守恒量及其在场论中的应用

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

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.

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.