PHYSICAL STATES IN MATTER-COUPLED DILATON GRAVITY

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.