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arXiv 2311.06910gr-qchep-lathep-th
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聚焦宇宙:探寻量子时空

Zooming in on the Universe: In Search of Quantum Spacetime

Joren Brunekreef

AI总结:

该论文研究低维非微扰量子引力模型,提出基于量子Ricci曲率的曲率剖面可观测量,并应用于CDT及矩阵模型,最后介绍CDT模拟实践。

摘要:

本论文研究了非微扰量子引力的低维模型,特别关注因果动力学三角剖分(CDT)。我们定义了所谓的曲率剖面,这是一种基于量子Ricci曲率的新的量子引力可观测量。随后,我们在一类具有孤立曲率奇点的规则二维多边形上研究了其粗粒化能力,并确定了具有环面拓扑的(1+1)维CDT的曲率剖面。接下来,我们专注于2+1维CDT,研究二维空间切片几何的行为。然后,我们将注意力转向矩阵模型,探索一矩阵和二矩阵系综积分的微分重构。最后,我们提供了CDT量子引力计算机模拟的实践入门介绍。

英文摘要:

This thesis investigates low-dimensional models of nonperturbative quantum gravity, with a special focus on Causal Dynamical Triangulations (CDT). We define the so-called curvature profile, a new quantum gravitational observable based on the quantum Ricci curvature. We subsequently study its coarse-graining capabilities on a class of regular, two-dimensional polygons with isolated curvature singularities, and we determine the curvature profile of (1+1)-dimensional CDT with toroidal topology. Next, we focus on CDT in 2+1 dimensions, intvestigating the behavior of the two-dimensional spatial slice geometries. We then turn our attention to matrix models, exploring a differential reformulation of the integrals over one- and two-matrix ensembles. Finally, we provide a hands-on introduction to computer simulations of CDT quantum gravity.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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