Static Quantization of Two-dimensional Dilaton Gravity and Black Holes

Two-dimensional matterless dilaton gravity is a topological theory and can be classically reduced to a (0+1)-dimensional theory with a finite number of degrees of freedom. If quantization is performed, a simple gauge invariant quantum mechanics is obtained. The properties of the gauge invariant operators and of the Hilbert space of physical states can be determined. In particular, for N-dimensional pure gravity with (N-2)-dimensional spherical symmetry, the square of the ADM mass operator is self-adjoint, not the mass itself.