Hawking radiation and back-reaction in a unitary theory of 2D quantum gravity

We construct a manifestly unitary quantum theory of the CGHS model of 2D dilaton gravity by performing a reduced phase space quantization. It is shown that physical states exist such that in the semiclassical limit the Hawking radiation is present. A new method for calculating the back-reaction corrections to the classical metric is introduced, based on the expansion of the metric operator in a power series of the matter energy-momentum tensor operator. The first order correction to a local black hole mass function is evaluated, and it agrees with the expected semiclassical behaviour. We briefly discuss the calculation of higher-order corrections and implications for the quantum fate of a 2D black hole.