EXACT DIRAC QUANTIZATION OF ALL 2D DILATON GRAVITY THEORIES

The most general dilaton gravity theory in 2 spacetime dimensions is c onsidered. A Hamiltonian analysis is performed and the reduced phase s pace, which is two dimensional, is explicitly constructed in a suitabl e parametrization of the fields. The theory is then quantized via the Dirac method in a functional Schrodinger representation. The quantum c onstraints are solved exactly to yield the (spatial) diffeomorphism in variant physical wave functionals for all theories considered. These w ave functionals depend explicitly on the single configuration space co ordinate as well as on the imbedding of space into spacetime (i.e. on the choice of time).