  We give a general expression for the static potential energy of the
gravitational interaction of two massive particles, in terms of an invariant
vacuum expectation value of the quantized gravitational field. This formula
holds for functional integral formulations of euclidean quantum gravity,
regularized to avoid conformal instability. It could be regarded as the
analogue of the Wilson loop of gauge theories and allows in principle, through
numerical lattice simulations or other approximation techniques, non
perturbative evaluations of the potential or of the effective coupling
constant.
