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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.

目前的研究项目旨在基于“纯规范模型”分析有望在杨-米尔斯理论和量子引力理论中发挥作用的非微扰动力学。 “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配置A_<mu>=g^+E_<mu>g，并将度量场限制为g_<munu>(x)=E_<mu>xi^<alpha>(x)配置而得到的一种拓扑场论。引力理论中的 E_<nu>xi^<beta> (x) h_<alphabeta> (xi (x))。上学年，我们成功地开发了一种摄动展开方法，该方法从纯规范模型出发，相继纳入了与规范变换正交的规范场A_<mu>的涨落。我们还尝试将纯规范模型应用于量子引力，以解决“四维量子引力中具有不间断的广义坐标变换不变性的相位是否可能？”这一问题。本学年，我们继续进行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，我们尚未得到明确的答案，仍在继续研究：（1）虽然如果背景时空是四球体，我们得到了与杨-米尔斯理论相同的纯规范模型，但平坦背景对应的纯规范模型是一个自由理论，没有非平凡的动力学。（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量。作为与本项目没有直接关系的其他研究，我们开展了以下工作并发表了论文。 (1) Rindler时空弦场理论构建及弦热化分析。 (2)协变弦场论中的因果关系分析。