Computing the graph-changing dynamics of loop quantum gravity

TL;DR

This paper introduces a novel numerical method to implement and analyze the full graph-changing dynamics in loop quantum gravity, revealing new solutions and behaviors of quantum geometric observables.

Contribution

It develops a numerical tool that captures the full graph-changing action of the Hamiltonian constraint in LQG, advancing understanding of its phenomenology.

Findings

New solutions to the Hamiltonian constraint were found.

Quantum geometric observables behave differently with full graph-changing dynamics.

The numerical method can be applied to other domains.

Abstract

In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, { which acts on the spin network states modifying both spins and graphs.} Fixed-graph approximations of the dynamics have been extensively studied, but its full graph-changing action so far remains elusive. The latter, alongside the solutions of its constraint, are arguably the missing features { in canonical LQG to access phenomenology in all its richness}. Here, we discuss a recently developed numerical tool that, for the first time, implements graph-changing dynamics via the Hamiltonian constraint. We explain how it is used to find new solutions to that constraint and to show that some quantum geometric observables behave differently than in the graph-preserving truncation. We also point out that these new numerical methods can find applications in other domains.