引力量子化是当前基础物理研究中一个十分重要而困难的课题。圈量子引力方案作为最忠实于广义相对论的引力量子化方案，坚决贯彻执行广义相对论的核心思想- - 广义协变性原理，从而在世界范围内受到越来越多的重视。在当前圈量子引力理论的发展中，最重要的核心问题是量子动力学及其半经典分析。本项目致力于这两大重要且密切相关的研究课题，力图在其中做出实质性的贡献。具体内容包括：（1）建立圈量子引力中两种主要量子化形式（Spin-Foam形式与正则形式）的对应关系，从而由理论内部的自洽性来检验以及进一步完善圈量子引力理论；（2）分析Spin-Foam形式的半经典性质，包括费曼传播子的计算以及Spin-Foam振幅的量子修正；通过与经典理论以及量子场论的对比检验以及进一步完善圈量子引力理论。

Searching for a quantum theory of gravity is a major challenge in today's fundamental physics. Among several approaches to quantum gravity, Loop Quantum Gravity receives a growing worldwide recognition for its taking the central lesson of general relativity seriously: general covariance.This project mainly focuses on the key problems of Loop Quantum Gravity: quantum dynamics and semiclassical analysis. Concretely, this project is planed to contribute the following aspects: (1) to investigate the relation between the covariant Spin-Foam formulation and the canonical formulation of Loop Quantum Gravity, in order to test or/and improve the theory via self-consistency; (2) to investigate the semiclssical behavior of the Spin-Foam amplitude in the low-energy regime, in particular, to calculate the n-point Feynman propagator and to give the quantum corrections from the Spin-Foam formulation, in order to test or/and improve the theory via comparing with the classical theory and quantum field theory.