Integrating geometry in general 2D dilaton gravity with matter

General 2d dilaton theories, containing spherically symmetric gravity and h ence the Schwarzschild black hole as a special case, are quantized by an ex act path integral of their geometric (Cartan) variables. Matter, represente d by minimally coupled massless scalar fields is treated in terms of a syst ematic perturbation theory. The crucial prerequisite for our approach is th e use of a temporal gauge for the spin connection and for light-cone compon ents of the zweibeins which amounts to an Eddington-Finkelstein gauge for t he metric. We derive the generating functional in its most general form whi ch allows a perturbation theory in the scalar fields. The relation of the z ero order functional to the classical solution is established. As an exampl e we derive the effective (gravitationally) induced 4-vertex for scalar fie lds. (C) 1999 Elsevier Science B.V.