发表机构
School of Mathematical and Physical Sciences, University of Sheffield（谢菲尔德大学数学与物理科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用欧几里得 Regge 微积分离散化 Henneaux-Teitelboim 引力，在对称性约化的宇宙学模型中验证了连续极限可用单模时间定义，为量子引力的离散路径积分表述迈出第一步。
AI 中文摘要
Henneaux-Teitelboim 引力是单模引力的微分同胚不变形式，它在局部上等价于广义相对论，但包含一个额外的边界变量——单模时间，其在超曲面之间的差值度量了所包围的 4-体积。一般而言，单模版本的量子引力可以预期会偏离基于广义相对论的理论，但 Henneaux-Teitelboim 引力的离散路径积分表述尚未建立。在本文中，我们使用欧几里得 Regge 微积分的方法对 Henneaux-Teitelboim 引力进行离散化。在一个对称性约化的 Regge 宇宙学模型中测试该框架，我们重现了先前文献中的结果，并证明了连续极限可以自然地使用单模时间而非固有时间来定义。由于单模时间作为边界数据出现，而不是作为体中的自由度，这种方法允许将一般的单纯形三角剖分（超越高度对称的离散化）与连续体进行比较。我们的工作为 Henneaux-Teitelboim 引力的离散路径积分表述提供了第一步，并为时间作为量子引力中的边界变量增添了新的视角。
英文摘要
Henneaux-Teitelboim gravity is a diffeomorphism-invariant formulation of unimodular gravity that is locally equivalent to general relativity but includes an extra boundary variable, unimodular time, whose difference between hypersurfaces measures the enclosed 4-volume. In general, unimodular versions of quantum gravity can be expected to deviate from theories based on general relativity, but a discrete path-integral formulation for Henneaux-Teitelboim gravity has not yet been established. In this paper, we discretise Henneaux-Teitelboim gravity using the methods of Euclidean Regge calculus. Testing this framework in a symmetry-reduced model of Regge cosmology, we reproduce results in previous literature and demonstrate that the continuum limit can be naturally defined using unimodular time rather than proper time. Because unimodular time appears as boundary data as opposed to being a degree of freedom in the bulk, this approach allows for the comparison of general simplicial triangulations, beyond highly symmetric discretisations, to the continuum. Our work provides a first step towards a discrete path-integral formulation of Henneaux-Teitelboim gravity and adds a new perspective on time as a boundary variable in quantum gravity.
Comments30 pages, 9 figures
