中文摘要：

作为量子引力论的一种重要的候选理论,圈量子引力已取得了长足的进展.当今圈量子引力研究的一个核心而艰巨的课题是如何建立合理的量子动力学,具体到圈量子引力的正则形式中,动力学问题集中体现为合理构造密顿约束算符以及求解相应的约束方程.本文介绍了圈量子引力的基本思想以及圈量子引力中量子动力学研究的最新进展.新进展侧重于哈密顿约束算符的构造及其所定义的希尔伯特空间.

英文摘要：

As an important alternative quantum theory of general relativity,loop quantum gravity has made considerable progress. At present,a key and difficult issue in loop quantum gravity is to build a reasonable quantum dynamics. In the canonical formulation of loop quantum gravity,it requires us to construct a reasonable Hamiltonian constraint operator and then solve the quantum constraint equation. In this paper,we will review the basic ideas of loop quantum gravity and its quantum dynamics. We will mainly focus on the construction of Hamiltonian constraint operators and the corresponding Hilbert spaces in which the Hamiltonian constraint operators can be well defined.