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 Tavernelli 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. (shrink)

A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of (...) Quantum Gravity. (shrink)