Coherent spin-networks
arXiv:0912.4054 · doi:10.1103/PhysRevD.82.024012
Abstract
In this paper we discuss a proposal of coherent states for Loop Quantum Gravity. These states are labeled by a point in the phase space of General Relativity as captured by a spin-network graph. They are defined as the gauge invariant projection of a product over links of Hall's heat-kernels for the cotangent bundle of SU(2). The labels of the state are written in terms of two unit-vectors, a spin and an angle for each link of the graph. The heat-kernel time is chosen to be a function of the spin. These labels are the ones used in the Spin Foam setting and admit a clear geometric interpretation. Moreover, the set of labels per link can be written as an element of SL(2,C). Therefore, these states coincide with Thiemann's coherent states with the area operator as complexifier. We study the properties of semiclassicality of these states and show that, for large spins, they reproduce a superposition over spins of spin-networks with nodes labeled by Livine-Speziale coherent intertwiners. Moreover, the weight associated to spins on links turns out to be given by a Gaussian times a phase as originally proposed by Rovelli.
15 pages
References in corpus (11)
- LQG vertex with finite Immirzi parameter
- A new spinfoam vertex for quantum gravity
- A New Spin Foam Model for 4d Gravity
- Twisted geometries: A geometric parametrisation of SU(2) phase space
- The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
- The complete LQG propagator: II. Asymptotic behavior of the vertex
- Group Integral Techniques for the Spinfoam Graviton Propagator
- Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
- Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
- Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
- Semiclassical analysis of the Loop Quantum Gravity volume operator: Area Coherent States
Cited by in corpus (72)
- The Spin Foam Approach to Quantum Gravity
- A Short Review of Loop Quantum Gravity
- Twisted geometries: A geometric parametrisation of SU(2) phase space
- Polyhedra in loop quantum gravity
- Towards Spinfoam Cosmology
- Realistic Observable in Background-Free Quantum Gravity: the Planck-Star Tunnelling-Time
- Loop quantum gravity: the first twenty five years
- On the geometry of loop quantum gravity on a graph
- Spinning Loop Black Holes
- Lorentzian spinfoam propagator
- Lifting SU(2) Spin Networks to Projected Spin Networks
- Cosmological constant in spinfoam cosmology
- A spin foam model for general Lorentzian 4-geometries
- A new look at loop quantum gravity
- Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
- Quantum Reduced Loop Gravity: Semiclassical limit
- General relativistic statistical mechanics
- A proposed proper EPRL vertex amplitude
- Quantum Gravity: A Brief History of Ideas and Some Prospects
- Spinfoams in the holomorphic representation
- Loop Quantum Gravity Vacuum with Nondegenerate Geometry
- Many-nodes/many-links spinfoam: the homogeneous and isotropic case
- Cosmological Coherent State Expectation Values in LQG I. Isotropic Kinematics
- Loop Quantum Gravity
- Spectral dimension of quantum geometries
- Quantum Reduced Loop Gravity: a realistic Universe
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
- Simple model for quantum general relativity from loop quantum gravity
- Super-Group Field Cosmology
- Euclidean three-point function in loop and perturbative gravity
- A Homogeneous Model of Spinfoam Cosmology
- Loop expansion and the bosonic representation of loop quantum gravity
- Numerical computations of next-to-leading order corrections in spinfoam large- asymptotics
- Noether's Charge in the Super-Group Field Cosmology
- Twisted Geometries Coherent States for Loop Quantum Gravity
- Learning about Quantum Gravity with a Couple of Nodes
- Polytopes in all dimensional loop quantum gravity
- Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
- Perelomov type coherent states of SO(D + 1) in all dimensional loop quantum gravity
- Squeezed vacua in loop quantum gravity
- Coherent states for FLRW space-times in loop quantum gravity
- Thermally correlated states in Loop Quantum Gravity
- Rainbow-like Black Hole metric from Loop Quantum Gravity
- Superposition type coherent states in all dimensional loop quantum gravity
- Area Law from Loop Quantum Gravity
- Holonomy-flux spinfoam amplitude
- Geometric parametrization of phase space of all dimensional loop quantum gravity
- Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
- One vertex spin-foams with the Dipole Cosmology boundary
- Continuous formulation of the Loop Quantum Gravity phase space
- The effective dynamics of weak coupling loop quantum gravity
- Towards a Loop Quantum Gravity and Yang-Mills Unification
- Searching for Coherent States: From Origins to Quantum Gravity
- Semiclassical Loop Quantum Gravity and Black Hole Thermodynamics
- Spin foam amplitude of the black-to-white hole transition
- A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
- Coherent State Operators in Loop Quantum Gravity
- Algorithmic approach to Cosmological Coherent State Expectation Values in LQG
- Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property
- Numerical approach to the black-to-white hole transition
- Spinfoam cosmology with the proper vertex amplitude
- Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
- Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
- On the gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity
- Dynamics in canonical models of loop quantum gravity
- Spin foam propagator: A new perspective to include a cosmological constant
- Including topology change in Loop Quantum Gravity with topspin network formalism with application to homogeneous and isotropic cosmology
- Partial absence of cosine problem in 3d Lorentzian spin foams
- A Model of Spinfoam Coupled with an Environment
- Spinfoam tunneling of quantum geometries in angle variables
- Loop quantum gravity with optimal control path integral, and application to black hole tunneling
- Nonlocal correlations for semiclassical states in loop quantum gravity