Vacuum correlations at geodesic distance in quantum gravity

The vacuum correlations of the gravitational field are highly non-trivial to be defined and computed, as soon as their arguments and indices do not belong to a background but become dynamical quantities. Their knowledge is essential however in order to understand some physical properties of quantum gravity, like virtual excitations and the possibility of a continuum limit for lattice theory. In this review the most recent perturbative and non-perturbative advances in this field are presented. (To appear on Riv. Nuovo Cim.)Comment: report U.T.F. 332, July 94. Plain TeX, 67 pp. (+ 1 table and 7 figures, available from the author