2-dimensional Regge gravity in the conformal gauge

By restricting the functional integration to the Regge geometries, we give the discretized version of the well known path integral formulation of a-dimensional quantum gravity in the conformal gauge. We analyze the role played by diffeomorphisms in the Regge framework and we give an exact expression for the Faddeev-Popov determinant related to a Regge surface; such an expression in the smooth limit goes over to the correct continuum result.