Abstract
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.)
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