Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators

TL;DR

This paper reformulates spin networks in Loop Quantum Gravity as harmonic oscillators, linking quantum geometry to quantum information and non-commutative geometry, offering new insights into the semi-classical limit.

Contribution

It introduces a harmonic oscillator representation of spin networks and connects holographic degrees of freedom to matrix models, advancing the quantum information perspective in LQG.

Findings

Spin networks are reformulated as harmonic oscillators.

Holographic degrees of freedom are described by matrix models.

Provides a new perspective on the semi-classical limit of LQG.

Abstract

Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the theory are described as matrix models. This allow us to make a link with non-commutative geometry and to look at the issue of the semi-classical limit of LQG from a new perspective. This work is thought as part of a bigger project of describing quantum geometry in quantum information terms.