Instantons in the Quantum Framework of 2D Gravity

Abstract

We analyze the non--perturbative features of 2D quantum gravity defined by stochastic regularization of the unstable matrix model showing, first, that the WKB approximation of the well-defined quantum Fokker-Planck hamiltonian corresponds to the semiclassical eigenvalue density of the former. The double scaled potential exhibits an instanton--like behaviour, which is universal and scales, but whose interpretation in terms of pure gravity is still open.