DIRAC CONSTRAINT QUANTIZATION OF A DILATONIC MODEL OF GRAVITATIONAL COLLAPSE

We present an anomaly-free Dirac constraint quantization of the string -inspired dilatonic gravity (the CGHS model) in an open two-dimensiona l spacetime. We show:that the quantum theory has the same degrees of f reedom as the classical theory, namely, all the modes of the scalar fi eld on an auxiliary flat background, supplemented by a single addition al variable corresponding to the primordial component of the black hol e mass. The functional Heisenberg equations of motion for these dynami cal variables and their canonical conjugates are linear, and they have exactly the same form as the corresponding classical equations. A can onical transformation brings us back to the physical geometry and indu ces its quantization.