Lattice Loop Quantum Gravity

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.

3 figures

References in corpus (2)

• Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
• On Semi-Classical States of Quantum Gravity and Noncommutative Geometry

Cited by in corpus (3)

• Modular Theory, Non-Commutative Geometry and Quantum Gravity
• C*-algebras of Holonomy-Diffeomorphisms & Quantum Gravity I
• Algebras of Quantum Variables for Loop Quantum Gravity, I. Overview