Quantization of Space-Time and Gravitational Field

量子引力的研究有两个主要目的，一是量子化引力子，实现可重整化的量子引力场理论;二是量子宇宙学，创造时空。对于第一个主题，我们采用了一种数值方法，称为动力学三角形的单纯引力进行量子化的爱因斯坦广义相对论，非微扰。对于第二个问题，我们将动力学三角剖分方法推广到d维（d= 2，3，4）流形上，并利用d维圆盘体积与（d-1）维边界表面积的关系定义了适合于该拓扑的时间。将空间坐标系嵌入到d球上，通过测地距离定义距离。为了检验算法的正确性，利用边界刘维尔场论的解析解和二维矩阵模型，通过测量d维圆盘上最后一个散射面上的两点标量曲率相关，分析了宇宙微波背景辐射的各向异性。它与WRAP使命观察到的两点温度相关性在质量上是一致的。

Study of quantum gravity has two major purposes, firstly quantizing graviton to achieve a renormalizable quantum field theory of gravity, and secondly the quantum cosmology to create space-time. For the first topics we employ a numerical method known as the dynamical triangulation of the simplicial gravity to perform quantization of the Einstein general relativity, non-perturbatively. As for the second subject the dynamical triangulation is extended to create d-dimensional (d=2,3, and 4) manifold with the open topology of disk.Time is defined proper to the topology through the relation between the d-dimensional disk volume and the (d-1)-dimensional boundary surface area. Space coordinate system is embedded on the d-sphere with the distance defined through geodesic distance. In order to check the correctness of algorithm analytical solutions of the boundary Liouville field theory and the matrix models in 2-dimension are utilized.The method is applied to analyze the anisotropies of the cosmic microwave background by measuring the 2-point scalar curvature correlation on the last scattering surface created in the d-dimensional disk. It shows qualitative agreement to the 2-point temperature correlation observed by the WRAP mission.