We revisit the quantization of matter-coupled, two-dimensional dilaton
gravity. At the classical level and with a cosmological term, a serie
s of held transformations leads to a set of free fields of indefinite
signature. Without matter the system is represented by two scalar fiel
ds of opposite signature. With a particular quantization for the scala
r with negative kinetic energy, the system has zero central charge and
we find some physical states satisfying all the Virasoro conditions.
With matter, the constraints cannot be solved because of the Virasoro
anomaly. We discuss two avenues for consistent quantization: modificat
ion of the constraints, and BRST quantization. The first avenue appear
s to lead to very few physical states. The second, which roughly corre
sponds to satisfying half of the Virasoro conditions, results in a ric
h spectrum of physical states. This spectrum however, differs signific
antly from that of free matter fields propagating on flat two-dimensio
nal space-time. (C) 1996 Academic Press, Inc.