ar X iv : h ep - l at / 9 60 80 55 v 1 1 2 A ug 1 99 6 1 Correlation functions in lattice formulations of quantum gravity ∗

There are two related schools attempting at a lattice theory of quantum gravity, dynamical triangulation and Regge quantum gravity. We concentrate on the latter approach and refer to [1,2] for excellent reviews of the former framework. In particular we investigate different formulations, all of them based on the original work by Regge [3], namely conventional Regge gravity [4,5], a group theoretical approach [6], Z2link Regge-theory [7], and Regge gravity coupled to SU(2)-gauge theory [8]. Each model exposes phase transitions at some critical gravitational couplings separating small and large curvature phases and allows to look for a continuum limit. [9,10]. A candidate realistic quantum theory of gravity should reproduce the expected long range interaction behavior observed in nature. Thus we calculate two-point funtions to probe the existence of massless quanta of the gravitational field.