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。在本项目中，Masao Ninomiya主要研究了量子重力的以下两个主题：（1）在时空中，在2个维度附近的2+ epsilondonmentions的时空中，我们应用了非驱动性场理论的方法，其中使用了Rernnalization Group和Epsilon扩展。然后，我们试图提取应保持较高维度的通用性能，并最终旨在构建4个维度量子重力。实际上，与hikaru kawai（Kek，教授）和吉萨岛（Yoshihisa Kitazawa）（Tokyo Inst.Tech。弱耦合区域，一个附近的临界点和强耦合区域。我们发现，随机三角剖分的已知结果存在于强耦合区域。（2）在critcal点附近，我们使用肾脏化gruop得出了GR的候选……在短距离内更加行驶的理论。此外，我们发现了可观察到的缩放亲戚。（2）我们表明，通过在临时仪表中量化封闭环的长度的2维重力被降低到闭环长度的量子机械系统。我们进一步对系统进行了量化，并获得了没有动力学术语的预测哈密顿量。在这里获得的Thoery被认为是非关键维度的弦场理论。该方法为研究弦场理论提供了一个新的方向。这项研究是与Masafumi Fukuma（Yukawa Inst。，助理），Nobuyuki Ishibashi（Kek，Assoc.prof。）和Hikaru Kawai（Kek，Prof.）合作进行的。在本项目中，Masao Ninomiya不仅获得了服务器的重要结果，而且还提倡量子重力研究的新方向。2。 Kazuo Fujikawa提出了一种用于计算QCD.3中β功能的新方法。 Misao Sasaki在量子重力在宇宙创造中的作用中做出了一项重要的研究。较少的