Coherent states for FLRW space-times in loop quantum gravity
arXiv:1011.5676 · doi:10.1103/PhysRevD.83.044029
Abstract
We construct a class of coherent spin-network states that capture proprieties of curved space-times of the Friedmann-Lamaître-Robertson-Walker type on which they are peaked. The data coded by a coherent state are associated to a cellular decomposition of a spatial (const.) section with dual graph given by the complete five-vertex graph, though the construction can be easily generalized to other graphs. The labels of coherent states are complex $SL(2, \mathbbm{C})$ variables, one for each link of the graph and are computed through a smearing process starting from a continuum extrinsic and intrinsic geometry of the canonical surface. The construction covers both Euclidean and Lorentzian signatures; in the Euclidean case and in the limit of flat space we reproduce the simplicial 4-simplex semiclassical states used in Spin Foams.
10 pages, 1 figure, published version
References in corpus (48)
- Absence of Singularity in Loop Quantum Cosmology
- LQG vertex with finite Immirzi parameter
- Spin Foam Models for Quantum Gravity
- A new spinfoam vertex for quantum gravity
- A New Spin Foam Model for 4d Gravity
- Representations of the holonomy algebras of gravity and non-Abelian gauge theories
- Twisted geometries: A geometric parametrisation of SU(2) phase space
- Isotropic Loop Quantum Cosmology
- Lorentzian spin foam amplitudes: graphical calculus and asymptotics
- Asymptotic analysis of the EPRL four-simplex amplitude
- On the semiclassical limit of 4d spin foam models
- Graviton propagator from background-independent quantum gravity
- Gauge Field Theory Coherent States (GCS) : I. General Properties
- Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
- Homogeneous Loop Quantum Cosmology
- A "general boundary" formulation for quantum mechanics and quantum gravity
- Towards Spinfoam Cosmology
- The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
- Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
- Quantum gravity with a positive cosmological constant
- LQG propagator from the new spin foams
- From twistors to twisted geometries
- Quantum Spin Dynamics (QSD) : VII. Symplectic Structures and Continuum Lattice Formulations of Gauge Field Theories
- Coherent spin-networks
- EPRL/FK Group Field Theory
- Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type
- Particle scattering in loop quantum gravity
- On the geometry of loop quantum gravity on a graph
- Casting Loop Quantum Cosmology in the Spin Foam Paradigm
- Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme
- Towards the QFT on Curved Spacetime Limit of QGR. II: A Concrete Implementation
- Stepping out of Homogeneity in Loop Quantum Cosmology
- Self-energy and vertex radiative corrections in LQG
- Canonical Gravity with Fermions
- Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
- Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
- Spinfoams in the holomorphic representation
- Spin foams as Feynman diagrams
- The linearization of the Kodama state
- Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations
- Fermions in Loop Quantum Cosmology and the Role of Parity
- Numerical indications on the semiclassical limit of the flipped vertex
- Coherent States for Black Holes
- Asymptotics of LQG fusion coefficients
- Big Bounce in Dipole Cosmology
- Intertwiner dynamics in the flipped vertex
- Approximating the physical inner product of Loop Quantum Cosmology
- Detecting the non-universal gauge boson at high-energy collider
Cited by in corpus (13)
- Cosmological constant in spinfoam cosmology
- Quantum Reduced Loop Gravity: Semiclassical limit
- Discrete Gravity Models and Loop Quantum Gravity: a Short Review
- Many-nodes/many-links spinfoam: the homogeneous and isotropic case
- New Loop Quantum Cosmology Modifications from Gauge-covariant Fluxes
- Learning about Quantum Gravity with a Couple of Nodes
- Coherent states for quantum gravity: towards collective variables
- Anisotropic Spinfoam Cosmology
- Area Law from Loop Quantum Gravity
- Holonomy-flux spinfoam amplitude
- Semiclassical Loop Quantum Gravity and Black Hole Thermodynamics
- Towards a Loop Quantum Gravity and Yang-Mills Unification
- Spinfoam cosmology with the proper vertex amplitude