离散动力学：规范不变性和量子化
Discrete Dynamics: Gauge Invariance and Quantization
摘要：
考虑了离散动力系统的规范不变性及其与量子化的关系。为了完整地描述系统的规范对称性，我们明确地构造了一类以自然的方式统一了空间对称性和内部对称性的群。我们描述了与离散和有限背景有关的规范原理的主要特征。假设连续现象是更基本的离散过程的近似，我们讨论--借助一个简单的例子--这些过程和它们的连续近似之间的关系。我们提出了一种方法来引入量子结构的离散系统，基于有限规范群。在这种方法中，量子化可以解释为引入一种特殊的规范联结。我们说明了我们的方法量化一个简单的模型，并建议推广这个模型。我们研究的主要工具之一是用C语言编写的程序。
英文摘要：
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and internal symmetries. We describe the main features of the gauge principle relevant to the discrete and finite background. Assuming that continuous phenomena are approximations of more fundamental discrete processes, we discuss -- with the help of a simple illustration -- relations between such processes and their continuous approximations. We propose an approach to introduce quantum structures in discrete systems, based on finite gauge groups. In this approach quantization can be interpreted as introduction of gauge connection of a special kind. We illustrate our approach to quantization by a simple model and suggest generalization of this model. One of the main tools for our study is a program written in C.
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