We develop a transfer matrix formalism for two-dimensional pure gravity. By taking the continuum limit, we obtain a "Hamiltonian formalism" in which the geodesic distance plays the role of time. Applying this formalism, we obtain a universal function which describes the fractal structures of two dimensional quantum gravity in the continuum limit.

We construct the string field Hamiltonian for c = 1 -6 / m ( m + 1) string theory in the temporal gauge. In order to do so, we first examine the Schwinger-Dyson equations of the matrix chain models and propose the continuum version of them. The results of boundary conformal field theory are useful in making a connection between the discrete and continuum pictures. The W constraints are derived from the continuum Schwinger-Dyson equations. We also check that these equations are consistent with other known results about noncritical string theory. The string field Hamiltonian is easily obtained from the continuum Schwinger-Dyson equations. It looks similar to the Kaku-Kikkawa Hamiltonian and may readily be generalized to c > 1 cases.