Study for Construction of Quantum Theory of Gravity

从广义相对论中的引力理论出发，构造“量子引力理论”或“量子引力”是近代理论物理学的主要课题之一。二宫先生在过去几年中与河合教授（KEK）和北泽洋教授合作进行了研究（东京工业研究所），关于如何用基于重整化群和量子力学的统计场论方法构造量子引力理论的理论扩张.我们得到了几个结果，引起了注意，不仅在日本，而且在海外。我们开始研究2+ 1维的Einstein引力，在2维时空附近的Einstein引力是可量子化的，然后通过重整化群将所得理论推广到现实的4维时空，我们在1996年提出了两个方向的研究。其中之一是我们可以证明我们的量子引力理论的重整化，这是在过去的几年中得到的。这样，我们的量子引力理论使我们能够研究时空结构的短距离行为或高能行为。我们研究的第二个进展是，我们可以与Y.Kitazawa一起对大爆炸奇点附近的时空性质进行详细的研究，这表明宇宙的诞生。结果表明，时空具有标度性，自相似性成立。我们计划对如何构造四维量子引力进行研究，M. M.Wanuma证明了矩阵模型（格点引力）中的非微扰动力学变量是费米子变量，它确实代表了孤立子对象。他还获得了一些有趣的非微扰结果。

It is one of the main subjects in Modern Theoretical Physics to construct "Quantum Theory of Gravity" or "Quantum Gravity" from Gravitational Theory in General Theory of Relativity.M.Ninomiya studied in the past few years, in collaboration with Prof.H.Kawai (KEK) and Prof. Y.Kitazawa (Tokyo Inst.Technology), the theory as to how to construct Quantum Theory of Gravity by using the method of statistical field theory based on the renormalization group and epsilon expansion. We obtained several results which attracted attention not only in Japan but also overseas. Our method is unique in the sense that we begin to study the Einstein gravity in 2+epsilon dimensions near 2 dimensional space time where it becomes remormalizable, and then extend the resultant theory into realistic 4 dimensional space time through renormalization group.In 1996 we put forward our study in two directions. One of them is that we could prove renormalizability of our quantum gravity theory which was obtained in the past years. In this way our quantum gravity theory enables us to study the short distance behavior or high energy behavior of the space time structure. 2nd development in our study is that together with Y.Kitazawa we could perform the detail investigation of property of the space time near Big Bang singularity, which indicates birth of Universe. It is found that the space time has scaling property so that self-similarity holds. We plan to go to the study as to how to construct 4 dimensional Quantum Gravity.M.Fukuma showed that nonperturbative dynamical variables in matrix model (lattice gravity) is fermionic variable and it really represents solitonic object. He also obtained some interesting nonperturbative results.