  We present a gravitational quantum dynamics theory that combines quantum
field theory for particle dynamics in space-time with classical Einstein's
general relativity in a non-Riemannian Finsler space. This approach is based on
the geometrization of quantum mechanics proposed in ref. [1] and combines
quantum and gravitational effects into a global curvature of the Finsler space
induced by the quantum potential associated to the matter quantum fields. In
order to make this theory compatible with general relativity, the quantum
effects are described in the framework of quantum field theory, where a
covariant definition of `simultaneity' for many-body systems is introduced
through the definition of a suited foliation of space-time. As in Einstein's
gravitation theory, the particle dynamics is finally described by means of a
geodesic equation in a curved space-time manifold.
