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. BU-HEP 96-17 MIT-CTP-2544 July, 1996 ∗This work was supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contracts #DE-FG02-91ER40676 and #DE-FC02-94ER40818, and by Korea Science and Engineering Foundation (KOSEF).