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

本研究的目的是在“纯规范模型”的基础上，分析在杨-米尔斯理论和量子引力理论中可能起作用的非微扰动力学。“纯规范模型”是一种拓扑场论，它是通过在杨-米尔斯理论中将规范场限制在纯规范组态A&lt；Mu&gt；=g^+E_&lt；Mu&gt；g，并通过将度规场限制在组态g&lt；munu&gt；(X)=E&lt；Mu&gt；xi^&lt；α&gt；(X)E&lt；nu&gt；xi^&lt；beta&gt；(X)引力理论中的Alphabeta&gt；(xi(X))。在上一学年，我们成功地发展了一种微扰展开方法，它从纯规范模型出发，依次考虑了与规范变换垂直的规范场的涨落。我们还尝试将纯规范模型应用到量子引力中，以解决“在四维量子引力中是否可能存在具有未破缺的广义坐标变换不变性的位相？”的问题。在本学年，我们继续了将纯规范模型应用于量子引力的研究。然而，主要由于以下两个问题，我们还没有得到一个确定的答案，并且仍在继续研究：(1)当背景时空是四球时，虽然我们得到了与Yang-Mills理论相同的纯规范模型，但对应于平坦背景的纯规范模型是一个没有平凡动力学的自由理论。(2)我们不知道量子引力理论中什么是有物理意义的可观测数据。由于其他研究与本项目无关，我们开展了以下工作并发表了论文。(1)Rindler时空弦场论的建立和弦的热化分析。(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.