Analysis of the dynamics in gauge and quantum gravity theories using the pure-gauge model

本研究项目的目的是在“纯规范模型”的基础上，分析Yang-Mills理论和量子引力理论中可能出现的非微扰动力学。“纯规范模型”是将规范场A_<mu> (x)限制为杨-米尔斯理论中的纯规范构型A_<mu>=g^+E_<mu>g，将度量场限制为重力理论中的g_<mu > (x)=E_<mu>xi^< α > (x) E_<nu>xi^< β > (x) h_< α > (xi (x))得到的一种拓扑场论。在上一学年，我们成功地开发了一种微扰展开方法，该方法从纯规范模型出发，将规范场A_<mu>与规范变换正交的涨落先后纳入其中。我们还尝试将纯规范模型应用于量子引力，以解决“在四维量子引力中具有不破缺一般坐标变换不变性的相是否可能”的问题。＂．在本学年，我们继续研究将纯规范模型应用于量子引力。然而，主要由于以下两个问题，我们还没有得到一个明确的答案，仍在继续研究：(1)虽然在背景时空是四球的情况下，我们得到了与杨-米尔斯理论相同的纯规范模型，但与平坦背景对应的纯规范模型是一个没有非平凡动力学的自由理论。(2)我们不知道在量子引力理论中什么是物理上有意义的可观测值。作为与本项目不直接相关的其他研究，我们进行了以下工作并发表了论文。(1)基于Rindler时空的弦场理论构建及弦热化分析。(2)协变弦场理论中的因果关系分析。

The present research project aims at analyzing, on the basis of "pure-gauge model", non-perturbative dynamics expected to be working in Yang-Mills theory and quantum gravity theory. The "pure-gauge model" is a kind of topological field theory obtained by restricting the gauge field A_<mu> (x) to the pure-gauge configurations A_<mu>=g^+E_<mu>g in Yang-Mills theory, and by restricting the metric field to the configuration g_<munu> (x)=E_<mu>xi^<alpha> (x) E_<nu>xi^<beta> (x) h_<alphabeta> (xi (x)) in gravity theory. In the last academic year, we succeeded in developing a perturbation expansion method which, starting from the pure-gauge model, incorporates successively the fluctuations of the gauge field A_<mu> orthogonal to the gauge transformation. We also tried to apply the pure-gauge model to quantum gravity to solve the problem "Is the phase with unbroke general coordinate transformation invariance possible in four dimensional quantum gravity? ".In this academic year, we continued the research of applying the pure-gauge model to quantum gravity. However, due mainly to the following two problems, we have not yet obtained a definite answer and are still continuing the research : (1) Though we obtain the same kind of pure-gauge model as in Yang-Mills theory if the background space-time is a four sphere, the pure-gauge model corresponding to flat background is a free theory without non-trivial dynamics. (2) we do not know what are physically meaningful observables in quantum gravity theory.As other researches not directly related to the present project, we have carried out the followings and published the papers. (1) Construction of string field theory on Rindler space-time and analysis of string thermalization. (2) Analysis of causality in covariant string field theory.