Exact Path Integral Quantization of Generic 2-D Dilaton Gravity

Abstract

Local path integral quantization of generic 2D dilaton gravity is considered. Locality means that we assume asymptotic fall off conditions for all fields. We demonstrate that in the absence of `matter' fields to all orders of perturbation theory and for all 2D dilaton theories the quantum effective action coincides with the classical one. This resolves the apparent contradiction between the well established results of Dirac quantization and perturbative (path-integral) approaches which seemed to yield non-trivial quantum corrections. For a particular case, the Jackiw--Teitelboim model, our result is even extended to the situation when a matter field is present.