论文标题
重力的边缘模式 - I：角电位和电荷
Edge modes of gravity -- I: Corner potentials and charges
论文作者
论文摘要
这是一系列旨在理解重力系统边缘模式和对称性的经典性质和量子性质的系列文章。该分析的目的是：i）清楚地了解不同的重力表述如何提供角落对称代数的不同部门的非平凡表示，ii）为量子几何形状状态作为该角对称代数的表示状态的新提案的基础。在第一篇论文中，我们解释了重力的不同公式如何在公制和四型变量中共享相同的散装符号结构，但在角落有所不同，进而导致角对称代数的不相等表示。这为重力配方提供了一个组织标准，具体取决于在角落在拐角处非平常表示的物理对称群。该原理可以用作“宝藏图”，揭示了寻求量子重力的新线索和路线。基于这些结果，我们对[1]中的爱因斯坦 - 卡丹 - 霍尔斯特重力的角符号潜力和对称性进行了详细的分析，并使用它来对[2]中的简单性约束提供新的外观，并在[3]中处理量化。
This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different formulations of gravity provide non-trivial representations of different sectors of the corner symmetry algebra, and ii) set the foundations of a new proposal for states of quantum geometry as representation states of this corner symmetry algebra. In this first paper we explain how different formulations of gravity, in both metric and tetrad variables, share the same bulk symplectic structure but differ at the corner, and in turn lead to inequivalent representations of the corner symmetry algebra. This provides an organizing criterion for formulations of gravity depending on how big the physical symmetry group that is non-trivially represented at the corner is. This principle can be used as a "treasure map" revealing new clues and routes in the quest for quantum gravity. Building up on these results, we perform a detailed analysis of the corner symplectic potential and symmetries of Einstein-Cartan-Holst gravity in [1], use this to provide a new look at the simplicity constraints in [2], and tackle the quantization in [3].
