Dynamics for a 2-vertex Quantum Gravity Model
arXiv:1006.2451 · doi:10.1088/0264-9381/27/23/235010
Abstract
We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N) invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.
28 pages, v2: typos corrected
References in corpus (35)
- Quantum Nature of the Big Bang: Improved dynamics
- Absence of Singularity in Loop Quantum Cosmology
- Quantum Spin Dynamics (QSD)
- Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
- LQG vertex with finite Immirzi parameter
- Robustness of key features of loop quantum cosmology
- ``Sum over Surfaces'' form of Loop Quantum Gravity
- Loop quantum cosmology of k=1 FRW models
- Quantum Spin Dynamics (QSD) II
- Black hole entropy and SU(2) Chern-Simons theory
- Algebraic Quantum Gravity (AQG) I. Conceptual Setup
- Towards Spinfoam Cosmology
- Closed FRW model in Loop Quantum Cosmology
- Anti-deSitter universe dynamics in LQC
- Lectures on Quantum Black Holes
- Loop Quantization of Vacuum Bianchi I Cosmology
- Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
- U(N) Coherent States for Loop Quantum Gravity
- Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology
- The Fine Structure of SU(2) Intertwiners from U(N) Representations
- Quantum Black Holes: Entropy and Entanglement on the Horizon
- Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
- Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity
- Loop Quantum Cosmology II: Volume Operators
- Stepping out of Homogeneity in Loop Quantum Cosmology
- Cosmic recall and the scattering picture of Loop Quantum Cosmology
- The combinatorics of the SU(2) black hole entropy in loop quantum gravity
- The flat FRW model in LQC: the self-adjointness
- Physical time and other conceptual issues of QG on the example of LQC
- Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations
- Bulk Entropy in Loop Quantum Gravity
- Black holes in full quantum gravity
- A State Sum Model for (2+1) Lorentzian Quantum Gravity
- The 6j-symbol: Recursion, Correlations and Asymptotics
- Dynamics for a simple graph using the U(N) framework for loop quantum gravity
Cited by in corpus (38)
- Polyhedra in loop quantum gravity
- Spinor Representation for Loop Quantum Gravity
- From the discrete to the continuous - towards a cylindrically consistent dynamics
- Quantum-Reduced Loop Gravity: Cosmology
- U(N) tools for Loop Quantum Gravity: The Return of the Spinor
- Cosmological implications of interacting Group Field Theory models: cyclic Universe and accelerated expansion
- A new perspective on cosmology in Loop Quantum Gravity
- Quantum Reduced Loop Gravity: Semiclassical limit
- Group field theory condensate cosmology: An appetizer
- Holomorphic Lorentzian Simplicity Constraints
- Discrete Gravity Models and Loop Quantum Gravity: a Short Review
- Deformation Operators of Spin Networks and Coarse-Graining
- Twistor Networks and Covariant Twisted Geometries
- Many-nodes/many-links spinfoam: the homogeneous and isotropic case
- Classical Setting and Effective Dynamics for Spinfoam Cosmology
- Holonomy Operator and Quantization Ambiguities on Spinor Space
- Coarse graining as a representation change
- Group theoretical Quantization of Isotropic Loop Cosmology
- Generating Functions for Coherent Intertwiners
- On the Expansions in Spin Foam Cosmology
- The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity
- Loop gravity in terms of spinors
- Learning about Quantum Gravity with a Couple of Nodes
- 2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
- Observations on interfacing loop quantum gravity with cosmology
- Quantum simulations of a qubit of space
- Spinors and Twistors in Loop Gravity and Spin Foams
- Holomorphic Simplicity Constraints for 4d Riemannian Spinfoam Models
- Path integral renormalisation in loop quantum cosmology
- Classical dynamics for Loop Gravity: The 2-vertex model
- Renormalisation with SU(1, 1) coherent states on the LQC Hilbert space
- U(N) and holomorphic methods for LQG and Spin Foams
- Intertwiner Entanglement Excitation and Holonomy Operator
- Dynamics for a simple graph using the U(N) framework for loop quantum gravity
- From loop quantum gravity to cosmology: the two-vertex model
- New tools for Loop Quantum Gravity with applications to a simple model
- U(N) invariant dynamics for a simplified Loop Quantum Gravity model
- Cosmology in Loop Quantum Gravity: symmetry reduction preserving gauge degrees of freedom