Abstract

The problem of how to put interactions in two-dimensional quantum gravity in the strong coupling regime is studied. It shows that the most general interaction consistent with this symmetry is a Liouville term that contains two parameters (?,?) satisfying the algebraic relation 2?-?=2 in order to assure the closure of the diffeomorphism algebra. The model is classically soluble and it contains as a general solution the temporal singularity. The theory is quantized and we show that the propagation amplitude falls to zero in ?=0. This result shows that the classical singularities are smoothed by quantum effects and the big-bang concept could be considered as a classical extrapolation instead of a physical concept.