  Two-dimensional matterless dilaton gravity with arbitrary dilatonic potential
can be discussed in a unitary way, both in the Lagrangian and canonical
frameworks, by introducing suitable field redefinitions. The new fields are
directly related to the original spacetime geometry and in the canonical
picture they generalize the well-known geometrodynamical variables used in the
discussion of the Schwarzschild black hole. So the model can be quantized using
the techniques developed for the latter case. The resulting quantum theory
exhibits the Birkhoff theorem at the quantum level.
