Gravitational quantum dynamics: a geometrical perspective

TL;DR

This paper introduces a novel gravitational quantum dynamics theory that integrates quantum field theory with Einstein's general relativity within a Finsler geometric framework, aiming to unify quantum and gravitational effects.

Contribution

It proposes a new geometrical approach combining quantum mechanics and gravity in a non-Riemannian Finsler space, extending the geometrization of quantum mechanics to include gravitational effects.

Findings

Quantum effects induce a global curvature in Finsler space.

Particle dynamics follow geodesic equations in a curved space-time.

The theory aligns quantum field effects with classical general relativity.

Abstract

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.