标题： 具有缩放约束的规范三阶张量模型 显示英文标题

标题： A canonical rank-three tensor model with a scaling constraint

摘要： 一个在正则形式中的三阶张量模型最近被提出。 该模型通过一组第一类约束描述模糊空间的一致局部时间演化，这些约束在壳上形成具有结构函数的闭合代数。 实际上，该代数为广义相对论正则形式中的狄拉克-德维特约束代数提供了代数一致的离散化。 然而，该模型的配置空间包含表示相同模糊空间的明显退化。 在本文中，为了删除这些退化，添加了另一个代表标度对称性的第一类约束，以提出一个新的正则三阶张量模型。 结果是，虽然之前模型的经典解通常表现出发散或消失的行为，新模型具有紧致的配置空间，其经典解在时间演化中渐近地趋于固定点或循环轨道。 其中，固定点包含具有群对称性的配置，可能代表静态对称模糊空间。 还讨论了局部哈密顿约束唯一性的问题，并给出一个唯一的最小正则张量模型。 显示英文摘要

摘要： A rank-three tensor model in canonical formalism has recently been proposed. The model describes consistent local-time evolutions of fuzzy spaces through a set of first-class constraints which form an on-shell closed algebra with structure functions. In fact, the algebra provides an algebraically consistent discretization of the Dirac-DeWitt constraint algebra in the canonical formalism of general relativity. However, the configuration space of this model contains obvious degeneracies of representing identical fuzzy spaces. In this paper, to delete the degeneracies, another first-class constraint representing a scaling symmetry is added to propose a new canonical rank-three tensor model. A consequence is that, while classical solutions of the previous model have typically runaway or vanishing behaviors, the new model has a compact configuration space and its classical solutions asymptotically approach either fixed points or cyclic orbits in time evolution. Among others, fixed points contain configurations with group symmetries, and may represent stationary symmetric fuzzy spaces. Another consequence on the uniqueness of the local Hamiltonian constraint is also discussed, and a minimal canonical tensor model, which is unique, is given.