约束Hamilton系统的积分因子和守恒量及其在场论中的应用

Abstract

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

CLC Number:

O369

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

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