Functional Schrödinger and BRST quantization of (1+1)-dimensional gravity

We discuss the quantization of pure string-inspired dilaton gravity in 1+1 dimensions, and of the same theory coupled to scalar matter. We perform the quantization using the functional Schrödinger and BRST formalisms. We find, both for pure gravity and the matter-coupled theory, that the two quantization procedures give inequivalent "physical" results.