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It is shown that the 1+1-dimensional matter-coupled Jackiw-Teitelboim modeland the model with an exponential potential can be converted by means ofappropriate canonical transformations into a bosonic string theory propagatingon a flat target space with an indefinite signature. This makes it possible toconsistently quantize these models in the functional Schroedingerrepresentation thus generalizing recent results on CGHS theory.Comment: 15 pages, Late

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