Fundamental Research of the Theory of Quantum Gravity.

1. 在本项目中，Masao Ninomiya主要研究了以下两个关于量子引力的课题：(1)在2+ epsilon维的时空中，我们采用了非微扰场论的方法，其中重新化群和epsilon展开一起使用。然后，我们试图提取出应该在高维中存在的普遍性质，并最终致力于构建四维量子引力。事实上，与Hikaru Kawai（KEK，教授）和Yoshihisa Kitazawa（东京工业大学）合作。(1)我们证明了在2+ ε维量子引力中存在一个紫外稳定不动点，并且存在3个相；弱耦合区、临界点附近的耦合区和强耦合区。我们发现随机三角剖分的已知结果在强耦合区域成立。(2)在临界点附近，利用重整化群导出了近距离gr . More航空理论的候选模型。此外，我们还发现了观测值之间的标度关系。(2)通过将二维引力在时间规范中量子化，证明了二维引力可以简化为闭环长度的量子力学系统。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理论。从而为弦场理论的研究提供了一个新的方向。这项研究是与Masafumi Fukuma（汤川研究所，助理），Nobuyuki Ishibashi （KEK，副教授）和Hikaru Kawai （KEK，教授）合作完成的。在目前的项目中，Masao Ninomiya不仅取得了几项重要成果，而且还倡导了量子引力研究的新方向。Kazuo Fujikawa在QCD.3中提出了一种计算beta函数的新方法。佐佐木Misao Sasaki对量子引力在宇宙形成中的作用做了重要的研究。少

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