A strategy for addressing this problem has been suggested; the idea is to study the boundary amplitude, namely a path integral over a finite space-time region, seen as a function of the boundary value of the field. In conventional quantum field theory, this boundary amplitude is well–defined and codes the physical information of the theory; it does so in quantum gravity as well, but in a fully background–independent manner. A generally covariant definition of formula_394-point functions can then be based on the idea that the distance between physical points –arguments of the formula_394-point function is determined by the state of the gravitational field on the boundary of the spacetime region considered.