Constraint Algebra in Causal Loop Quantum Gravity

TL;DR

This paper develops a de-Broglie--Bohm causal interpretation of canonical quantum gravity using Ashtekar variables, analyzing the algebra of constraints and how quantum effects modify classical relations.

Contribution

It introduces a de-Broglie--Bohm framework for quantum gravity with Ashtekar variables and derives the modified Poisson brackets of constraints.

Findings

Poisson brackets of constraints are derived in the quantum context.

The Poisson bracket of the Hamiltonian with itself is altered by quantum effects.

Classical constraint algebra is modified in the de-Broglie--Bohm interpretation.

Abstract

de-Broglie--Bohm causal interpretation of canonical quantum gravity in terms of Ashtekar new variables is built. The Poisson brackets of (deBroglie--Bohm) constraints are derived and it is shown that the Poisson bracket of Hamiltonian with itself would change with respect to its classical counterpart.