论文标题
重力威尔逊循环的几何通量公式
Geometric flux formula for the gravitational Wilson loop
论文作者
论文摘要
在普朗克量表上找到差异不变的可观察到的可观察到的表征重力和时空的特性对于在量子重力方面取得进展至关重要。 Levi-Civita连接的全能和Wilson环路是量子曲率可观察物的构建中潜在有趣的成分。由于最新的非扰动量子重力的发展，我们在有限回路的整体和某些曲率积分之间建立了三个和四个维度的新关系。它们比Nonabelian Stokes的定理的引力版本要简单得多，但需要在歧管中存在完全测量的表面，这是由于存在合适的杀伤向量而遵循的。我们表明，由于存在保守的几何通量，这种关系在平滑的表面变形下是不变的。
Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at the Planck scale is essential for making progress in quantum gravity. The holonomy and Wilson loop of the Levi-Civita connection are potentially interesting ingredients in the construction of quantum curvature observables. Motivated by recent developments in nonperturbative quantum gravity, we establish new relations in three and four dimensions between the holonomy of a finite loop and certain curvature integrals over the surface spanned by the loop. They are much simpler than a gravitational version of the nonabelian Stokes' theorem, but require the presence of totally geodesic surfaces in the manifold, which follows from the existence of suitable Killing vectors. We show that the relations are invariant under smooth surface deformations, due to the presence of a conserved geometric flux.
