Implement dynamics and identify a semiclassical sector in loop quantum gravity

Establish a consistent implementation of dynamics in loop quantum gravity and identify a semiclassical sector that connects the theory with smooth solutions to Einstein’s equations, thereby addressing the main open problems recognized in the loop quantum gravity and loop quantum cosmology programs.

Background

The paper situates its contribution within the broader context of loop quantum gravity (LQG) and loop quantum cosmology (LQC). While LQC has achieved several successes, the authors emphasize that foundational issues in LQG remain unresolved: specifically, how to implement dynamics and how to identify a semiclassical sector that recovers smooth general-relativistic spacetimes.

Their paper of the two-vertex model and its U(N)-symmetric reduction is motivated in part by these outstanding challenges, aiming to bridge full LQG with effective cosmological dynamics and illuminate aspects of the semiclassical regime.