标题： 最简单的规范形式的Regge演算模型 显示英文标题

标题： The simplest Regge calculus model in the canonical form

摘要： 三维(3D)流形在连续时间中的动力学被考虑。该流形是闭合的，由两个具有对应顶点识别的四面体组成。模型的作用量是从完全离散的四维Regge微积分的广义相对论(GR)作用量通过极限过程得到的。它在Hilbert-Palatini(HP)形式中与连续广义相对论作用量非常相似，但具有有限数量的自由度。该理论的正则结构被描述。中心问题是出现新的关系，这些关系包含时间导数，不是从拉格朗日量中得出的，而是用来确保系统完全离散的四维Regge微积分起源。特别是，考虑到这些因素对于获得真正的自由度数量是必要的，即在给定时刻的三维Regge流形的边长数量。 显示英文摘要

摘要： Dynamics of a Regge three-dimensional (3D) manifold in a continuous time is considered. The manifold is closed consisting of the two tetrahedrons with identified corresponding vertices. The action of the model is that obtained via limiting procedure from the general relativity (GR) action for the completely discrete 4D Regge calculus. It closely resembles the continuous general relativity action in the Hilbert-Palatini (HP) form but possesses finite number of the degrees of freedom. The canonical structure of the theory is described. Central point is appearance of the new relations with time derivatives not following from the Lagrangian but serving to ensure completely discrete 4D Regge calculus origin of the system. In particular, taking these into account turns out to be necessary to obtain the true number of the degrees of freedom being the number of linklengths of the 3D Regge manifold at a given moment of time.