Spacetime-noncommutativity regime of Loop Quantum Gravity

TL;DR

This paper connects Loop Quantum Gravity's effective spacetime modifications in the Minkowski regime to the $k$-Minkowski noncommutative spacetime, offering a new perspective on quantum spacetime structure.

Contribution

It demonstrates that the symmetry algebra modifications in Loop Quantum Gravity align with the $k$-Minkowski noncommutative spacetime framework.

Findings

Symmetry algebra modifications are consistent with $k$-Minkowski spacetime.

Supports the relevance of noncommutative spacetime in quantum gravity.

Bridges Loop Quantum Gravity with noncommutative geometry approaches.

Abstract

A recent study by Bojowald and Paily provided a path toward the identification of an effective quantum-spacetime picture of Loop Quantum Gravity, applicable in the "Minkowski regime", the regime where the large-scale (coarse-grained) spacetime metric is flat. A pivotal role in the analysis is played by Loop-Quantum-Gravity-based modifications to the hypersurface deformation algebra, which leave a trace in the Minkowski regime. We here show that the symmetry-algebra results reported by Bojowald and Paily are consistent with a description of spacetime in the Minkowski regime given in terms of the $\kappa$-Minkowski noncommutative spacetime, whose relevance for the study of the quantum-gravity problem had already been proposed for independent reasons.