Study for Construction of Quantum Theory of Gravity

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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.