BRST ANALYSIS OF PHYSICAL STATES FOR 2D GRAVITY COUPLED TO C-LESS-THAN-OR-EQUAL-TO-1 MATTER

We consider 2D gravity coupled to c less-than-or-equal-to 1 conformal matter in the conformal gauge. The Liouville system is represented by a free scalar field, phi(L), with background charge such that the BRST operator imposing reparametrization invariance is nilpotent. We compute the cohomology of this BRST charge on the product of the Fock space of phi(L) with those of the ghosts and one other free scalar field, phi(M), representing the matter system. From this calculation the physical states of the full theory are determined. For the c < 1 case the further projection from the Fock space of phi(M) to the irreducible representation, using Felder's resolution, reproduces the results of Lian and Zuckerman.