Quantization of string theory for $c\le 1$

Abstract

We consider the canonical quantization scheme for $c\le 1$ ($(p,q)$ -) string theories and compare it with what is known from matrix model approach. We derive explicitly a trivial ($\equiv$ topological) solution. We discuss a ``dressing" operator which in principle allows one to obtain a non-trivial solution, but an explicit computation runs into a problem of analytic continuation of the formal expressions for $\tau$-functions. We discuss also the application of proposed scheme to the case of discrete matrix model and consider some parallels with mirror symmetry and background independence in string theory.

(talk given by A.M. at the $XXVII$th International Symposium on Elementary particle physics, Wendisch-Rietz, Germany (September 1993)), latex 12 pp