Neo Formulation of Quantum Gravity and its Dynamical Aspects.

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Recently I have been working on two different kinds of subjects : (1)Various applications of generalized gauge theory, which was formulated from generalized Chern-Simons theory. (2)Fractal structures of quantum gravity, numerical and analytical investigations. There are already several results in our investigations but they are not yet in the form of published papers. This is partly because of my moving time from Tokyo to Sapporo for last one or two ysars.(1)We have succeeded to generalize the standard Chern-Simons action in arbitrary dimensions. In the generalized gauge thoery approach, we have investigated how the quantization of our generalized Chern-Simons theory works. We have succeeded to quantize gl (1, R) generalized Chern-Simons action in two dimensions. The model is simple but highly non-trivial for the quantization because of the reducibility of the model. The most recent result in this direction is the connection of the generalized Chern-Somons gauge theory to non-commutative algebra formulation of Yang-Mills action. We have shown that Weinberg-Salam model can be formulated in the generalized version of of ourgauge thory and have a direct connection with non-commmutative algebra formulation of gauge thorey. The theory is formulated in particular only by formsincluding matter fields.(2)In our previous work we have shown numerically that the fractal sructure is the fundamental nature of quantum gravity for c=-2 model in two dimensions. In the later analytic investigations we have scceeded to obtain transfer matrix of two dimensional quantum surface, which makes it possible to calculate the fractal dimension of two-demensional gravity for c=0 model.Recently we have started another type of munerical investigations on two-dimensional quantum gravity surface. This is an investigation of studying fractal structure from finite size scaling points of view.