Generalization of Bohmian Mechanics and Quantum Gravity Effective Action

TL;DR

This paper extends Bohmian mechanics to quantum gravity using effective actions, enabling the derivation of field configurations and trajectories in a quantum gravitational context, bridging quantum mechanics and gravity.

Contribution

It introduces a natural generalization of de Broglie-Bohm theory to quantum gravity via effective actions, avoiding certain quantum uncertainties and classical trajectory issues.

Findings

Effective action formalism allows for field configuration calculations in quantum gravity.

The approach bridges Bohmian mechanics with quantum gravity using path integrals.

Field configurations lead to particle trajectories in quantum gravitational settings.

Abstract

We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action equations of motion, which is beneficial even in the non-gravitational case, since in this way one avoids the violations of the Heisenberg uncertainity relations and the absence of the classical trajectories for stationary bound states. Another advantage of the effective action formalism is that one can obtain the field configurations in the case of a quantum field theory (QFT). The proposed QG generalization is natural for Bohmiam mechanics because a dBB wavefunction is really a wavefunction of the Universe and in order to define the effective action for an arbitrary initial state one needs a QG path integral. The QG effective action can be constructed by using the piecewise flat quantum gravity (PFQG) theory and the PFQG effective action can be approximated by the QFT effective action for General Relativity coupled to matter, with a cutoff determined by the average edge length of the spacetime triangulation. One can then calculate the corresponding field configurations and from these field configurations one can obtain the trajectories for the corresponding elementary particles.