标题： 在Regge演算中的Hilbert作用量 显示英文标题

标题： The Hilbert Action in Regge Calculus

摘要： 希尔伯特作用量是为单纯几何推导出来的。 我通过将单纯几何分解为由单纯（Delaunay）格子及其对偶（Voronoi）格子定义的四维单元，从而恢复了通常的雷吉计算作用量。 在单纯几何中，黎曼标量曲率、固有四维体积以及因此而来的雷吉作用量被证明是精确的，这意味着作用量的定义不需要引入平均过程，或者像以往所有推导中常见的连续度量序列。 看起来，这两种对偶格子几何的统一是雷吉计算的一个显著特征。 显示英文摘要

摘要： The Hilbert action is derived for a simplicial geometry. I recover the usual Regge calculus action by way of a decomposition of the simplicial geometry into 4-dimensional cells defined by the simplicial (Delaunay) lattice as well as its dual (Voronoi) lattice. Within the simplicial geometry, the Riemann scalar curvature, the proper 4-volume, and hence, the Regge action is shown to be exact, in the sense that the definition of the action does not require one to introduce an averaging procedure, or a sequence of continuum metrics which were common in all previous derivations. It appears that the unity of these two dual lattice geometries is a salient feature of Regge calculus.