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

使用纯规范模型分析规范和量子引力理论的动力学

基本信息

批准号：
07640394
负责人：
HATA Hiroyuki
金额：
$ 1.02万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640394/
关键词：
gauge theory quantum gravity color confinement BRST mon-perturbative effect topological field theory string field theory

项目摘要

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.

本研究计划的目的是在“纯规范模型”的基础上，分析杨-米尔斯理论和量子引力理论中的非微扰动力学。“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组态A_<mu>=g^+E_<mu>g，将度规场限制为引力理论中的组态g_<munu>（x）=E_<mu>xi^<alpha>（x）E_<nu>xi ^<beta>（x）h_<alphabeta>（xi（x））而得到的一种拓扑场论。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，依次加入了与规范变换正交的规范场A_的涨落<mu>。我们还尝试将纯规范模型应用到量子引力中，以解决“四维量子引力中具有完整广义坐标变换不变性的相是否可能存在”的问题。本学年，我们继续开展了纯规范模型在量子引力中的应用研究。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）如果背景时空是一个四球，虽然我们得到了与杨-米尔斯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有物理意义的可观测量，作为与本项目没有直接关系的其他研究，我们进行了以下工作并发表了论文。(1)Rindler时空上弦场论的构造与弦热化的分析。(2)协变弦场论中的因果关系分析。