Free fields via canonical transformations of matter-coupled two-dimensional dilaton gravity models

It is shown that the (1+1)-dimensional matter-coupled Jackiw-Teitelboim model and the model with an exponential potential can be converted by means of appropriate canonical transformations into a theory of free fields with an indefinite metric. This makes it possible to consistently impose all the Virasoro constraints in the functional Schrödinger representation, thus generalizing recent results on the CGHS theory.