Spin Foam Models for Quantum Gravity

本项目关注的是量子引力理论背景下的动力学问题，称为{\em环量子引力}（LQG）。LQG是一种很有前途的方法，可以构建统一的自然描述，调和广义相对论原理（在大尺度上控制引力现象）和量子力学原理（在微观尺度上控制物质现象）。在LQG方面取得了重要进展，使人们对空间和时间的基本组成部分的性质有了简单的理解。例如，该理论预测，空间本身在微观尺度上是离散的，由基本构件构成。空间是由基本物体以类似于晶体材料中原子的晶格结构的方式构成的。我的工作旨在了解这些基本成分的动态，即它们如何相互作用和进化。这是该方法在很大程度上仍未解决的问题。在由普朗克长度给出的极小的长度尺度上，量子引力的影响被认为是重要的。理解这些机制中的现象对于解决早期宇宙的物理问题（为什么宇宙进化成我们今天看到的样子？），空间和时间的结构以及强引力场的物理（例如在黑洞奇点附近）等基本问题非常重要。理论理解将为目前不明显的问题提供新的见解，从而导致实验测试和未来可能的应用。

This project is concerned with the problem of dynamics in the context of the theory of quantum gravity known as {\em loop quantum gravity} (LQG). LQG is a promising approach to the construction of a unified description of nature that would reconcile the principles of general relativity (governing gravitational phenomena at large scales) and the principles of quantum mechanics (governing material phenomena at microscopic scales). Important progress has been achieved in LQG leading to a simple understanding of the nature of the fundamental constituents of space and time. For example the theory predicts that space itself is discrete at the microscopic scales and constructed out of fundamental building blocks. Space is constituted by basic objects in a way that resembles the lattice structure of {\em atoms} in a crystalline material. My work aims at understanding the dynamics of these fundamental constituents, i.e., how they interact and evolve. This is an issue that remains unsolved to a large extend in the approach.The effects of quantum gravity are expected to be important at the extremely small length scalegiven by the Planck length. Understanding of phenomena in these regimes is very important for addressing issues concerning the physics of the early universe (why does the universe has evolved into what we see today?), the structure of space and time, and the physics of strong gravitational fields (e.g. near a black hole singularity) among other fundamental questions. Theoretical understanding would provide new insight into questions that are not apparent at present leading to experimental tests and possible applications in the future.