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 (\ensuremath{\alpha},\ensuremath{\beta}) satisfying the algebraic relation 2\ensuremath{\beta}-\ensuremath{\alpha}=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 \ensuremath{\tau}=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. \textcopyright{} 1996 The American Physical Society.
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