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.

本研究项目旨在基于“纯正模型”分析，预计将在Yang-Mills理论和量子重力理论中起作用的非扰动动力学。 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)重力理论中的e__ <nu> xi^<beta>（x）H_ <alphabeta>（xi（x））。在上一学年，我们成功地开发了一种扰动扩展方法，该方法从纯模型开始，依次结合了量规场A_ <mu>正交对量规变换的波动。我们还试图将纯仪模型应用于量子重力，以解决问题：“在四维量子重力中，是否可以使用Unbroke一般坐标转换不变性？”。在本学年，我们继续研究将纯仪模型应用于量子重力的研究。但是，主要是由于以下两个问题，我们尚未获得明确的答案，并且仍在继续进行研究：（1）尽管我们获得了与Yang-Mills理论相同类型的纯柱模型，如果背景时空是四个领域，但与平面背景相对应的纯仪表模型是没有非易于动力学的自由理论。（2）我们不知道量子重力理论中物理上有意义的可观察力是什么。与其他研究与本项目无直接相关的其他研究，我们已经执行了以下内容并发表了论文。（1）关于林德勒时空和弦热分析的弦场理论的构建。（2）协变字段理论中因果关系的分析。