Generalized 2d-Dilaton Models, the True Black Hole and Quantum Integrability

All 1 + 1 dimensional dipheomorphism-invariant models can be viewed in a unified manner. This includes also general dilaton theories and especially spherically symmetric gravity (SSG) and Witten's dilatonic black hole (DBH). A common feature --- also in the presence of matter fields of any type --- is the appearance of an absolutely conserved quantity C which is determined by the influx of matter. Only for a subclass of generalized dilaton theories the singularity structure vanishes together with C. Such `physical' theories include, of course, SSG and DBH. It seems to have been overlooked until recently that the (classical) 'black hole' singularity of the DBH deviates from SSG in a physically nontrivial manner. At the quantum level for all generalized dilaton theories --- in the absence of matter --- the local quantum effects are shown to disappear. This enables us to compute e.g. the second loop order correction to the Polyakov term. For non-minimal scalar coupling we also believe to ..