NOTE ON THE SEMICLASSICAL APPROXIMATION IN QUANTUM-GRAVITY

We reexamine the semiclassical approximation for quantum gravity in th e canonical formulation, focusing an the definition of a quasiclassica l state for the gravitational field. It is shown that a state with cla ssical correlations must be a superposition of states of the form e(iS ) In terms of a reduced phase-space formalism, this type of state-can be expressed as a coherent superposition of eigenstates of operators t hat commute with the constraints and so correspond to constants of the motion. Contact is made witt the usual semiclassical approximation by showing that a superposition of this kind can be approximated by a WK B state with an appropriately localized prefactor. A qualitative analy sis is given of the effects of geometry fluctuations, and the possibil ity of a breakdown of the semiclassical approximation due to interfere nce between neighboring classical trajectories is discussed. It is sho wn that a breakdown in the semiclassical approximation can be a coordi nate-dependent phenomenon, as has been argued to be the case close to a black hole horizon.