标题： 't Hooft 的多边形方法的双曲重新研究 显示英文标题

标题： 't Hooft's Polygon Approach Hyperbolically Revisited

摘要： 多边形方法中(2+1)D引力与点粒子耦合的初始数据受到顶点方程和粒子方程的约束。 我们确定了顶点方程的双曲性质并推导了一些结果。 特别是我们能够将双曲运动群识别为连续理论中微分同胚的离散类似物。 我们表明点粒子也可以“双曲地”包含进来，但它们会破坏规范不变性。 最后我们推导出一致的初始数据集。 显示英文摘要

摘要： The initial data in the polygon approach to (2+1)D gravity coupled to point particles are constrained by the vertex equations and the particle equations. We establish the hyperbolic nature of the vertex equations and derive some consequences. In particular we are able to identify the hyperbolic group of motions as discrete analogues of the diffeomorphisms in the continuum theory. We show that particles can be included ``hyperbolically'' as well, but they spoil the gauge invariance. Finally we derive consistent sets of initial data.