CDT方程的半经典解分析

Semiclassical and Continuum Limits of Four-Dimensional CDT

This article discusses the infrared and the (perspective) ultraviolet limits of four-dimensional Causal Dynamical Triangulations (CDT). CDT is a non-perturabtive and background-independent approach to quantization of Einstein's gravity, based on a lattice regularization of the quantum-gravitational path integral. It is shown that inside the, so-called, de Sitter phase one recovers a four-dimensional semiclassical universe, where behaviour of the scale factor is consistent with classical solutions of Einstein's field equations and fluctuations of the scale factor are very accurately described b…

The phase structure and effective action of 3D CDT at higher spatial genus

We perform a detailed investigation of the phase structure and the semiclassical effective action of (2+1)-dimensional Causal Dynamical Triangulations (CDT) quantum gravity using computer simulations. On the one hand, we study the effect of enlarging the ensemble of triangulations by relaxing the simplicial manifold conditions in a controlled way. On the other hand, we cast a first look at CDT geometries with spatial topology beyond that of the sphere or torus. We measure the phase structure of the model for several triangulation ensembles and spatial topologies, finding evidence that the phas…

Causal Dynamical Triangulations in the Spincube Model of Quantum Gravity

We study the implications of the simplicity constraint in the spincube model of quantum gravity. By relating the edge-lengths to the integer areas of triangles, the simplicity constraint imposes very strong restrictions between them, ultimately leading to a requirement that all 4-simplices in the triangulation must be almost mutually identical. As a surprising and unexpected consequence of this property, one can obtain the CDT state sum as a special case of the spincube state sum. This relationship brings new insight into the long-standing problem of the relationship between the spinfoam appro…

因果动态三角剖分的半经典极限

The Semiclassical Limit of Causal Dynamical Triangulations

先前的工作已经表明，因果动力学三角剖分（CDT）定义的量子引力理论的宏观结构与德西特宇宙的宏观结构是相容的。在强调严格的非微扰性质的半经典极限，我们提出了一个详细的研究的三卷数据，这使我们能够重新确认的de Sitter结构，表现出短距离离散化的影响，并作出第一次详细调查的存在下高阶曲率项的有效作用的比例因子。从技术上讲，我们使用了一种新的方法来固定模拟中的总四卷。

四维三角化中的杨-米尔斯拓扑

Yang--Mills topology on four-dimensional triangulations

研究四维SU(N)规范理论与引力在CDT方法中的拓扑分类，揭示拓扑在热化三角化中仅在C相出现，建立相与 semiclassical 空间的时间联系。

Phase structure of Causal Dynamical Triangulations in 4D

Causal Dynamical Triangulations (CDT) is a lattice approach to quantum gravity. CDT has rich phase structure, including a semiclassical phase consistent with Einstein's general relativity. Some of the observed phase transitions are second (or higher) order which opens a possibility of investigating the ultraviolet continuum limit. Recently a new phase with intriguing geometric properties has been discovered and the new phase transition is also second (or higher) order.