Integrating geometry in general 2D dilaton gravity with matter

General 2d dilaton theories, containing spherically symmetric gravity and hence the Schwarzschild black hole as a special case, are quantized by an exact path integral of their geometric (Cartan) variables. Matter, represented by minimally coupled massless scalar fields is treated in terms of a systematic perturbation theory. The crucial prerequisite for our approach is the use of a temporal gauge for the spin connection and for light-cone components of the zweibeins which amounts to an Eddington-Finkelstein gauge for the metric. We derive the generating functional in its most general form which allows a perturbation theory in the scalar fields. The relation of the zero order functional to the classical solution is established. As an example we derive the effective (gravitationally) induced 4-vertex for scalar fields. (C) 1999 Elsevier Science B.V.