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

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.

16 pages, revtex, 3 figures

Cited by in corpus (68)

• U(N) Coherent States for Loop Quantum Gravity
• Quantum Black Holes: Entropy and Entanglement on the Horizon
• The Fine Structure of SU(2) Intertwiners from U(N) Representations
• Toy Model for a Relational Formulation of Quantum Theory
• SU(N) Irreducible Schwinger Bosons
• Observables in Loop Quantum Gravity with a cosmological constant
• Gravitational edge modes: From Kac-Moody charges to Poincaré networks
• Dynamics for a 2-vertex Quantum Gravity Model
• Gluing polyhedra with entanglement in loop quantum gravity
• Semiclassical analysis of Wigner $3j$-symbol
• Holomorphic Simplicity Constraints for 4d Spinfoam Models
• Holomorphic Lorentzian Simplicity Constraints
• Deformation Operators of Spin Networks and Coarse-Graining
• Quantum reference frames and deformed symmetries
• Many-nodes/many-links spinfoam: the homogeneous and isotropic case
• Bohr-Sommerfeld Quantization of Space
• Towards the Turaev-Viro amplitudes from a Hamiltonian constraint
• Classical Setting and Effective Dynamics for Spinfoam Cosmology
• Deformations of Polyhedra and Polygons by the Unitary Group
• A Discrete and Coherent Basis of Intertwiners
• From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
• On the Implementation of the Canonical Quantum Simplicity Constraint
• Quantum hyperbolic geometry in loop quantum gravity with cosmological constant
• Holonomy Operator and Quantization Ambiguities on Spinor Space
• Irreducible SU(3) Schwinger Bosons
• Loop expansion and the bosonic representation of loop quantum gravity
• Quantum causal histories in the light of quantum information
• Generating Functions for Coherent Intertwiners
• Revisiting the Simplicity Constraints and Coherent Intertwiners
• Spinors and Voros star-product for Group Field Theory: First Contact
• Fisher Metric, Geometric Entanglement and Spin Networks
• A note on the secondary simplicity constraints in loop quantum gravity
• 2+1D Loop Quantum Gravity on the Edge
• Learning about Quantum Gravity with a Couple of Nodes
• Twisted Geometries Coherent States for Loop Quantum Gravity
• Typicality in spin network states of quantum geometry
• Modified Special Relativity on a fluctuating spacetime
• Canonical Transformations and Loop Formulation of SU(N) Lattice Gauge Theories
• Stabilizer entropy of quantum tetrahedra
• Squeezed vacua in loop quantum gravity
• Spinors and Twistors in Loop Gravity and Spin Foams
• Entropy in the Classical and Quantum Polymer Black Hole Models
• Quantum Surface and Intertwiner Dynamics in Loop Quantum Gravity
• Surface state decoherence in loop quantum gravity, a first toy model
• SO*(2N) coherent states for loop quantum gravity
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Loop Quantum Gravity and Quantum Information
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• Invariants, Projection Operators and $SU(N)\times SU(N)$ Irreducible Schwinger Bosons
• Local Observables in ${\mathrm{SU}}_q(2)$ Lattice Gauge Theory
• The geometry and entanglement entropy of surfaces in loop quantum gravity
• U(N) and holomorphic methods for LQG and Spin Foams
• Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
• Dynamics for a simple graph using the U(N) framework for loop quantum gravity
• Quantum information in loop quantum gravity
• From loop quantum gravity to cosmology: the two-vertex model
• Deformed Heisenberg charges in three-dimensional gravity
• Probing the Shape of Quantum Surfaces: the Quadrupole Moment Operator
• Generating Functionals for Spin Foam Amplitudes
• Curvature from multipartite entanglement in quantum gravity states
• Deformations of Lorentzian Polyhedra: Kapovich-Millson phase space and SU(1,1) Intertwiners
• U(N) invariant dynamics for a simplified Loop Quantum Gravity model
• Elementary Particles as Gates for Universal Quantum Computation
• Effective geometry of Bell-network states on a dipole graph
• Nonlocal correlations for semiclassical states in loop quantum gravity
• Polyhedron phase space using 2-groups: kappa-Poincare as a Poisson 2-group
• New insights in quantum geometry
• At the Corner of Space and Time