An approach to quantum gravity

A model for quantum gravity is presented by treating the light-cone structure of space-time as classical and the conformal factor as a quantum degree of freedom. The motivation and the details of the formalism are discussed. The approach is used to discuss the question of singularities in the cosmological models. It is shown that one can introduce the concept of stationary states for the quantum geometry, in analogy with the stationary states of simple quantum systems. The quantum stationary geometries (QSG's) avoid the classical singularities. The light-cone structure is determined by a set of equations involving the expectation values in the QSG concerned. The cosmological implications of the formalism, especially to matter creation, flatness, etc., are discussed. The theory is conformally invariant in the quantum level.