Three models of non-perturbative quantum-gravitational binding.

Known quantum and classical perturbative long-distance corrections to the Newton potential are extended into the short-distance regime using evolution equations for a `running' gravitational coupling, which is used to construct examples non-perturbative potentials for the gravitational binding of two particles. Its motivation stems from a desire to elucidate the mass dependence of binding energies found in previous numerical results within the Dynamical Triangulation approach to quantum gravity. Model-I is based on the complete set of the relevant Feynman diagrams. Its potential has a singularity at a distance below which it becomes complex and the system obtains black hole-like features. Model-II is based on a reduced set of diagrams and its coupling approaches a non-Gaussian fixed point as the distance is reduced. Energies and eigenfunctions are obtained and used in a study of time-dependent collapse (model-I) and bouncing (both models) of a spherical wave packet. Returning to Dynamical Triangulation with experience of possible mass dependencies of binding energies we obtain new estimates of the renormalized Newton coupling with an improved understanding of its systematic uncertainties. Mass renormalization is found to be partially describable by perturbation theory in the continuum.