标题： 约束系统的动力学结构 显示英文标题

标题： Dynamical Structure of Irregular Constrained Systems

摘要： 具有函数相关约束的动力系统（奇异性系统），对于这些系统标准的 Dirac 方法不能直接适用，本文对此进行了讨论。根据这些系统的约束曲面附近的特性，它们被分为两类基本类型。 如果奇异约束是多线性的（I型），那么有可能使系统正则化，从而使哈密顿描述和拉格朗日描述等价。 当约束是线性函数的幂（II型）时，正则化并不总是可能实现，并且哈密顿描述和拉格朗日描述可能是动态不等价的。 文中证明了当动能在速度上为不定二次型时，这两种形式之间的不等价性可能发生。 还表明 I 型系统可以随着时间从规则配置演化为奇异配置，而不会发生任何灾难性变化。 奇异性在非线性理论的线性化近似以及这类系统的量子化中具有重要意义。 这些问题与高维 Chern-Simons 理论的相关性也进行了讨论。 显示英文摘要

摘要： Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the constraint surface into two fundamental types. If the irregular constraints are multilinear (type I), then it is possible to regularize the system so that the Hamiltonian and Lagrangian descriptions are equivalent. When the constraints are power of a linear function (type II), regularization is not always possible and the Hamiltonian and Lagrangian descriptions may be dynamically inequivalent. It is shown that the inequivalence between the two formalisms can occur if the kinetic energy is an indefinite quadratic form in the velocities. It is also shown that a system of type I can evolve in time from a regular configuration into an irregular one, without any catastrophic changes. Irregularities have important consequences in the linearized approximation to nonlinear theories, as well as for the quantization of such systems. The relevance of these problems to Chern-Simons theories in higher dimensions is discussed.