Project/Area Number  03640268 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
核・宇宙線・素粒子

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
NINOMIYA Masao Kyoto University, Yukawa Institute for Theoretical Phys., Professor, 基礎物理学研究所, 教授 (40198536)

CoInvestigator(Kenkyūbuntansha) 
SASAKI Misao Kyoto University, Department of Physics, Associate Professor, 理学部, 助教授 (70162386)
FUJIKAWA Kazuo University of Tokyo, Department of Physics, Professor, 理学部, 教授 (30013436)

Project Fiscal Year 
1991 – 1993

Project Status 
Completed(Fiscal Year 1993)

Budget Amount *help 
¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1993 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1992 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Quantum Gravity / 2D Gravity / Renormalization Group / epsilon Expansion / String Theory / String Field Theory / QCD / Path Integral / 量子重力 / 2次元重力 / くりこみ群 / ε展開 / 弦理論 / 弦の場の理論 / 経路積分の量子化 / 量子動 / 格子動 / ランダム分割 / 膜の理論 / 2次元動 / 格子重力 
Research Abstract 
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
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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
