Cocycle Properties of String Theories on Orbifolds

We study cocycle properties of vertex operators and present an operator representation of cocycle operators, which are attached to vertex operators to ensure the duality of amplitudes. It is shown that this analysis makes it possible to obtain the general class of consistent string theories on orbifolds.Comment: 40 pages (Talk given at Workshop on ``Recent Developments in String and Field theory", Kyoto, Japan on September 9-12, 1991.

Analysis of the Wheeler-DeWitt Equation beyond Planck Scale and Dimensional Reduction

We solve the Wheeler-DeWitt equation for {\it four}-dimensional Einstein gravity as an expansion in powers of the Planck mass by means of a heat kernel regularization. Our results suggest that in the universe with a very small radius or with a very large curvature beyond a Planck scale expectation values of operators are reduced to calculations in a path integral representation of {\it three}-dimensional Einstein gravity.Comment: 9 pages, latex file, KOBE-TH-94-0