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Quantization of Space-Time and Gravitational Field

时空和引力场的量子化

基本信息

批准号：
15540261
负责人：
YUKAWA T.
金额：
$ 2.37万
依托单位：
The Graduate University for Advanced Studies
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

项目摘要

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.

研究量子引力有两个主要目的，一是量子化引力子，实现可重整化的量子引力场论；二是量子宇宙论，创造时空。对于第一个主题，我们采用一种称为单纯引力动态三角测量的数值方法来非扰动地执行爱因斯坦广义相对论的量子化。至于第二个主题，动态三角剖分被扩展以创建具有圆盘开放拓扑的 d 维（d=2,3 和 4）流形。通过 d 维圆盘体积和 (d-1) 维边界表面积之间的关系来定义适合该拓扑的时间。空间坐标系嵌入在 d 球面上，其距离通过测地距离定义。为了检验边界刘维尔场理论算法解析解的正确性，利用二维矩阵模型，通过测量d维圆盘中最后一个散射面的两点标量曲率相关性，分析宇宙微波背景的各向异性。它显示出与 WRAP 任务观测到的 2 点温度相关性的定性一致性。