Quantum Surface and Intertwiner Dynamics in Loop Quantum Gravity

Abstract

We introduce simple generic models of surface dynamics in loop quantum gravity (LQG). A quantum surface is defined as a set of elementary patches of area glued together. We provide it with an extra structure of locality (nearest neighbors), thought of as induced by the whole spin network state defining the 3d bulk geometry around the quantum surface. Here, we focus on classical surface dynamics, using a spinorial description of surface degrees of freedom. We introduce two classes of dynamics, to be thought as templates for future investigation of LQG dynamics with in mind the dynamics of quantum black holes. The first defines global dynamics of the closure defect of the surface, with two basic toy-models, either a dissipative dynamics relaxing towards the closure constraint or a Hamiltonian dynamics precessing the closure defect. The second class of dynamics describes the isolated regime, when both area and closure defect are conserved throughout the evolution. The surface dynamics is implemented through U(N) transformations and generalizes to a Bose-Hubbard Hamiltonian with a local quadratic potential interaction. We briefly discuss the implications of modeling the quantum black hole dynamics by a surface Bose-Hubbard model.

20 pages

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
• From twistors to twisted geometries
• U(N) tools for Loop Quantum Gravity: The Return of the Spinor
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Revisiting the Simplicity Constraints and Coherent Intertwiners
• Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy

Cited by in corpus (9)

• Intertwiner Entanglement on Spin Networks
• Bubble Networks: Framed Discrete Geometry for Quantum Gravity
• 2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
• Quantum simulations of a qubit of space
• Hidden Messenger from Quantum Geometry: Towards Information Conservation in Quantum Gravity
• From Coarse-Graining to Holography in Loop Quantum Gravity
• Loop Quantum Gravity's Boundary Maps
• Area Propagator and Boosted Spin Networks in Loop Quantum Gravity
• Probing the Shape of Quantum Surfaces: the Quadrupole Moment Operator