EXACT OPERATOR QUANTIZATION OF A MODEL OF 2-DIMENSIONAL DILATON GRAVITY

Exact operator quantization is performed of a model of two-dimensional dilaton gravity in Lorentzian spacetime, classically equivalent to th e one proposed by Callan, Giddings, Harvey, and Strominger, in the spe cial case with 24 massless matter scalars. This is accomplished by dev eloping a nonlinear and nonlocal quantum canonical transformation of b asic interacting fields into a set of free fields, rigorously taking i nto account the spatially closed boundary condition. The quantized mod el enjoys conformal invariance and the entire set of physical states a nd operators are obtained in the BRST formalism. In addition, a rather detailed discussion of the nature of the basic issues for exact treat ment of models of quantum gravity is provided.