论文标题
量子重力的曲率轮廓
Curvature profiles for quantum gravity
论文作者
论文摘要
在最近引入的量子RICCI曲率概念的基础上，并由非扰动量子重力的考虑，我们主张一种新的，全球可观察到的曲线度量空间，即曲率曲线。它是通过整合规模依赖性的准本地量子曲率曲率而获得的，因此也取决于粗粒度尺度。为了了解局部高斯曲率的分布如何反映在曲率曲线中，我们将其计算为具有孤立圆锥形奇异性的一类常规多边形。我们专注于四面体的情况，为此，我们对其测量学有良好的计算控制，并将其曲率曲线与光滑球体的曲率进行比较。两者是不同的，但在质量上相似，这证实了曲率曲线具有平均属性，从量子的角度来看，这很有趣。
Building on the recently introduced notion of quantum Ricci curvature and motivated by considerations in nonperturbative quantum gravity, we advocate a new, global observable for curved metric spaces, the curvature profile. It is obtained by integrating the scale-dependent, quasi-local quantum Ricci curvature, and therefore also depends on a coarse-graining scale. To understand how the distribution of local, Gaussian curvature is reflected in the curvature profile, we compute it on a class of regular polygons with isolated conical singularities. We focus on the case of the tetrahedron, for which we have a good computational control of its geodesics, and compare its curvature profile to that of a smooth sphere. The two are distinct, but qualitatively similar, which confirms that the curvature profile has averaging properties which are interesting from a quantum point of view.
