权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Fundamental Research of the Theory of Quantum Gravity.

量子引力理论的基础研究。

基本信息

批准号：
03640268
负责人：
NINOMIYA Masao
金额：
$ 0.77万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1993
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03640268/
关键词：
Quantum Gravity 2D Gravity Renormalization Group epsilon Expansion String Theory String Field Theory QCD Path Integral 量子動格子動ランダム分割膜の理論 2次元動格子重力

项目摘要

1. In the present project, Masao Ninomiya have mainly studied the following two subjects on the quantum gravity :(1) In the space time with 2+ epsilondimensions near 2 dimensions, we applied the method of the nonperturbative field theory in which the rernorTnalization group and the epsilon expansion are used together. We then tried to extract the universal properties which should hold in higher dimensions and finally aimed to construct the 4 dimensional quantum gravity. In fact, in collaboration with Hikaru Kawai(KEK, Prof.) and Yoshihisa Kitazawa (Tokyo Inst.Tech., Assoc.Prof.) we obtained the following results :(1) We showed that in 2+ epsilondimensional quantum gravity there exist an ultraviolet stable fixed point and that there appear 3 phases ; weak coupling region, the one near the critical point and the strong coupling region. We found that the known result in the random triangulation holds in the strong coupling region.(2) Near the critcal point we derived a candidate of the gr … More avitational theory at short distance using the renormalization gruop. Furthermore we found the scaling relatives among the observables.(2) We showed that 2 dimensional gravity is reduced to the quantum mechanical system of the lengths of the closed loops, by quantizing it in the temporal gauge. We further 2nd quantized the system and obtained the pregeometric Hamiltonian with no kinetic term. The obtained thoery here is considered to be the string field theory at the noncritical dimension. Thus our method provides a new direction for studying the string field theory. This study has been performed in collaboration with Masafumi Fukuma (Yukawa Inst., Assistant), Nobuyuki Ishibashi (KEK, Assoc.Prof.) and Hikaru Kawai (KEK, Prof.). In the present project Masao Ninomiya has not only obtained serveral important results, but also advocated a new direction of the research of quantum gravity.2. Kazuo Fujikawa proposed a new method for calculating the beta function in QCD.3. Misao Sasaki made an important study in the role of quantum gravity in the creation of the Universe. Less

1.二宫正夫在本项目中主要研究了以下两个问题：（1）在2+ ε维的近2维时空中，我们采用了非微扰场论的方法，即归一化群和非微扰展开相结合的方法。然后，我们试图提取应该在更高维度下保持的普适性质，并最终旨在构建四维量子引力。事实上，在与Hikaru Kawai（KEK，教授）和Yoshihisa Kitazawa（Tokyo Inst.Tech.，助理教授）（1）证明了在2+ ε维量子引力中存在一个紫外稳定的不动点，并且存在三个相：弱耦合区、临界点附近的相和强耦合区。我们发现在强耦合区域，随机三角剖分的已知结果成立。(2)在临界点附近，我们导出了一个候选的gr ...更多信息用重整化群研究近距离的引力理论。此外，我们还发现了观测量之间的缩放关系。(2)通过在时间规范中量子化二维引力，我们证明了二维引力被简化为闭环长度的量子力学系统。我们进一步对系统进行二次量子化，得到了不含动力学项的前几何哈密顿量。本文所得到的理论被认为是非临界维的弦场论。从而为弦场论的研究提供了一个新的方向。本研究是与Masafumi Jumuma（Yukawa Inst.，助理），Nobuyuki Ishibashi（KEK，助理教授）和Hikaru Kawai（KEK，Prof.）。二宫在本项目中不仅取得了几个重要的结果，而且提出了量子引力研究的一个新方向.藤川和夫提出了一种计算QCD中β函数的新方法。佐佐木美雄对量子引力在宇宙形成中的作用进行了重要研究。少