Exact operator quantization of a model of two-dimensional dilaton gravity

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