论文标题
奇异的拉格朗日人，受约束的哈密顿系统和量规不变性：dirac-bergmann算法的一个例子
Singular Lagrangians, Constrained Hamiltonian Systems and Gauge Invariance: An Example of the Dirac-Bergmann Algorithm
论文作者
论文摘要
Dirac-Bergmann算法是将奇异的Lagrangian转换为受约束的汉密尔顿系统的理论的根。受约束的哈密顿系统包括仪表理论 - 一般相对论，电磁，杨米尔斯，弦理论等。DIRAC-BERGMANN算法是优雅的，但同时相当复杂。它由许多通过一系列的推理链相连的大量逻辑步骤。文献中发现的Dirac-Bergmann算法的示例旨在隔离并说明其中一个或两个逻辑步骤。在本文中，我分析了一个有限维系统，该系统在算法中展示了所有主要步骤。该系统包括主要和次要约束，一等和二等的约束，对拉格朗日乘数的限制以及物理和衡量自由度。这个相对简单的系统提供了一个平台，用于讨论狄拉克的猜想，构建狄拉克支架并应用仪表条件。
The Dirac-Bergmann algorithm is a recipe for converting a theory with a singular Lagrangian into a constrained Hamiltonian system. Constrained Hamiltonian systems include gauge theories -- general relativity, electromagnetism, Yang Mills, string theory, etc. The Dirac-Bergmann algorithm is elegant but at the same time rather complicated. It consists of a large number of logical steps linked together by a subtle chain of reasoning. Examples of the Dirac-Bergmann algorithm found in the literature are designed to isolate and illustrate just one or two of those logical steps. In this paper I analyze a finite-dimensional system that exhibits all of the major steps in the algorithm. The system includes primary and secondary constraints, first and second class constraints, restrictions on Lagrange multipliers, and both physical and gauge degrees of freedom. This relatively simple system provides a platform for discussing the Dirac conjecture, constructing Dirac brackets, and applying gauge conditions.
