Fundamental Research of the Theory of Quantum Gravity.

1.在本项目中，野宫正雄主要研究了以下两个关于量子引力的课题：(1)在2+epsilon维近2维的时空中，我们应用了非微扰场理论的方法，其中结合了重正化群和epsilon展开。然后，我们试图提取在更高维度上应该保持的普遍性质，最终目标是构建四维量子引力。事实上，在与河井光(KEK，教授)的合作下，和Yoshihisa Kitazawa(东京理工学院副教授)结果表明：(1)在2+表观量子引力中，存在一个紫外光稳定不动点，并且存在三个相：弱耦合区、临界点附近的相和强耦合区。我们发现已知的随机三角剖分结果在强耦合区域内成立。(2)在临界点附近，我们推导了GR…的一个候选值使用重整化组的短距离更多的传态理论。通过在时间规范中的量子化，我们证明了二维引力可以简化为闭合环长的量子力学系统。我们进一步对系统进行了二次量子化，得到了不含动力学项的几何前哈密顿量。所得到的理论被认为是非临界维弦场论。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(Yukawa Inst，助理)，Nobuyuki Ishibashi(KEK，Asoc.教授)合作进行的。和Hikaru Kawai(KEK，教授)。在本项目中，二宫正夫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。藤川和夫在QCD中提出了一种计算贝塔函数的新方法。佐佐木美佐夫对量子引力在宇宙创造中的作用进行了重要研究。较少

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