New methods for analyzing quantum field theories

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We developed and applied several new methods for analyzing quantum field theories. In particular, we considered quantum gravity and string theories, and constructed useful nonperturbative frameworks for investigating those systems. First of all, we developed and epsilon - expansion scheme for 2+ epsilon dimensional quantum gravity. Using this scheme, we studied scaling properties of higher dimensional quantum gravity. We next considered R^2 Lagrangian can be solved exactly both in the infrared and ultraviolet limits. Furtheremore, we invented a transfer metrix formalism that can be applied in the presence of quantum fluctuations of the space-time. Using this method, we exactly solved the problem of two-dimensional quantum gravity, and proved that the space-time has fractal structures. This method may be a powerful tool for analyzing nonperturbative effects of string theories. Some attempts in this direction are now in progress.