标题： 离散时空格点上约束理论的规范量子化 显示英文标题

标题： Canonical quantization of constrained theories on discrete space-time lattices

摘要： 我们讨论在离散时空上表述的系统的规范量子化。 我们首先分析具有离散时间的简单机械系统的量子化。 当系统存在非完整约束时，量子化变得具有挑战性。 我们提出了一种新的规范形式和此类系统的量子化方法，这是通过离散规范变换来表述的。 这使得首次构建出具有离散时间的一般约束机械系统的规范形式。 我们将分析扩展到格点上的规范场论。 我们考虑了一个完整的规范形式，从离散作用量出发，对空间离散化的格点杨-米尔斯理论和空间与时间离散化的麦克斯韦理论进行分析。 在完成处理后，结果可以证明与传统转移矩阵方法的结果一致。 然后我们将该方法应用于BF理论，从而首次实现了对该理论的格点处理。 所提出的框架直接处理洛伦兹度规，而无需进行欧几里得旋转。 整个讨论被构造成一种形式，以便允许离散广义相对论的一致、明确的规范形式和量子化，这将在一篇即将发表的论文中进行讨论。 显示英文摘要

摘要： We discuss the canonical quantization of systems formulated on discrete space-times. We start by analyzing the quantization of simple mechanical systems with discrete time. The quantization becomes challenging when the systems have anholonomic constraints. We propose a new canonical formulation and quantization for such systems in terms of discrete canonical transformations. This allows to construct, for the first time, a canonical formulation for general constrained mechanical systems with discrete time. We extend the analysis to gauge field theories on the lattice. We consider a complete canonical formulation, starting from a discrete action, for lattice Yang--Mills theory discretized in space and Maxwell theory discretized in space and time. After completing the treatment, the results can be shown to coincide with the results of the traditional transfer matrix method. We then apply the method to BF theory, yielding the first lattice treatment for such a theory ever. The framework presented deals directly with the Lorentzian signature without requiring an Euclidean rotation. The whole discussion is framed in such a way as to provide a formalism that would allow a consistent, well defined, canonical formulation and quantization of discrete general relativity, which we will discuss in a forthcoming paper.