The Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory

TL;DR

This paper investigates the internal consistency of quantum geometrodynamics and quantum field theories within the Bohm-de Broglie interpretation, demonstrating their coherence and exploring implications for Lorentz invariance.

Contribution

It extends previous work by proving the consistency of Bohmian quantum cosmology and scalar field theories, including Lorentz invariance considerations, using a Hamiltonian approach.

Findings

Quantum geometrodynamics is consistent for any quantum potential.

Scalar field theory in Minkowski spacetime remains consistent under the Bohmian framework.

Lorentz invariance can be broken at the level of individual events in certain models.

Abstract

We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work [1], where a hamiltonian formalism for the bohmian trajectories was constructed, we show the consistency of the theory for any quantum potential, completing the scenarios for canonical quantum cosmology presented there. In the latter case, we prove the consistency of scalar field theory in Minkowski spacetime for any quantum potential, and we show, using this alternative hamiltonian method, a concrete example where Lorentz invariance of individual events is broken.