Spin Foam Models for Quantum Gravity

该项目关注量子引力理论（称为{\em loop quantum gravity}（LQG））背景下的动力学问题。LQG是一种很有前途的方法来构建一个统一的描述自然，将调和广义相对论的原则（在大尺度上的引力现象）和量子力学的原则（在微观尺度上的物质现象）。LQG已经取得了重要进展，导致对空间和时间的基本组成部分的性质的简单理解。例如，该理论预测，空间本身在微观尺度上是离散的，并且是由基本的构建块构成的。空间是由基本物体构成的，其构成方式类似于晶体材料中原子的晶格结构。 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。这是一个在很大程度上仍然没有解决的问题。量子引力的影响预计在普朗克长度给出的极小长度尺度上是重要的。理解这些机制中的现象对于解决有关早期宇宙物理学的问题非常重要（为什么宇宙演变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学（例如黑洞奇点附近）等基本问题。理论上的理解将为目前尚不明显的问题提供新的见解，从而导致未来的实验测试和可能的应用。

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.