Lattice Loop Quantum Gravity

TL;DR

This paper develops a separable version of Loop Quantum Gravity using cubic lattices, constructing semi-classical states with correct classical limits for key operators and constraints, and explores the continuum limit and diffeomorphism invariance.

Contribution

It introduces a new separable formulation of LQG with semi-classical states and operator constraints that match classical physics, and discusses the potential for a continuum limit.

Findings

Semi-classical states with correct classical limits constructed.

Hamilton and diffeomorphism constraints implemented as operators.

Discussion on the possibility of a continuum limit and restored diffeomorphism symmetry.

Abstract

We present a separable version of Loop Quantum Gravity (LQG) based on an inductive system of cubic lattices. We construct semi-classical states for which the LQG operators -- the flux, the area and the volume operators -- have the right classical limits. Also, we present the Hamilton and diffeomorphism constraints as operator constraints and show that they have the right classical limit. Finally, we speculate whether the continuum limit, which these semi-classical states probe, can be defined for the entire construction and thereby restore an action of the diffeomorphism group.