Constraints Algebra and Equations of Motion in Bohmian Interpretation of Quantum Gravity

TL;DR

This paper explores how quantum effects in Bohmian quantum gravity alter the constraints algebra, leading to covariant quantum Einstein's equations consistent with general coordinate transformations.

Contribution

It derives a modified constraints algebra in Bohmian quantum gravity and formulates covariant quantum Einstein's equations consistent with diffeomorphism invariance.

Findings

Quantum effects modify the constraints algebra in canonical gravity.

The new algebra aligns with projections of general coordinate transformations.

Quantum Einstein's equations are covariant under spatial and temporal diffeomorphisms.

Abstract

It is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general coordinate transformations to the spatial and temporal diffeomorphisms. The quantum Einstein's equations are derived and it is shown that they are manifestly covariant under the above diffeomorphisms, as it would be.