BOHM QUANTUM POTENTIALS AND QUANTUM-GRAVITY

A generally covariant theory, written in the spirit of Bohm's theory of quantum potentials, which applies to spinless, non interacting, gravitating systems, is formulated. In this theory the quantum state psi is coupled to the metric tensor g, and the effect of the "quantum potential" is absorbed in the geometry. At the same time, psi satisfies a covariant wave equation with respect to the very same g. This provides sufficient constraints to derive 11 coupled equations in the 11 unknowns: psi and the components of the metric tensor g-mu-v. The states of stable localized particles are identified, and vacuum-state solutions for both the Euclidean and the Lorentzian case are explicitly presented.