The projector on physical states in loop quantum gravity

Abstract

We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like, spacetime formalism for quantum gravity and relates this theory to the spin foam models. We also discuss how expectation values of physical quantity can be computed.

15 pages, 2 figures, substantially revised version

References in corpus (11)

• Loop Quantum Gravity
• Relativistic spin networks and quantum gravity
• Spin Foam Models
• Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories
• Quantum tetrahedra and simplicial spin networks
• On the consistency of the constraint algebra in spin network quantum gravity
• Loop constraints: A habitat and their algebra
• Causal evolution of spin networks
• Loop quantum gravity and quanta of space: a primer
• Matrix Elements of Thiemann's Hamiltonian Constraint in Loop Quantum Gravity
• Nonperturbative dynamics for abstract (p,q) string networks

Cited by in corpus (61)

• The Spin Foam Approach to Quantum Gravity
• Spin Foam Models for Quantum Gravity
• Flipped spinfoam vertex and loop gravity
• Observables in effective gravity
• Spacetime as a Feynman diagram: the connection formulation
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• Three dimensional loop quantum gravity: physical scalar product and spin foam models
• Loop quantum gravity: an outside view
• A spin foam model without bubble divergences
• Spin foam model for Lorentzian General Relativity
• Perfect discretization of reparametrization invariant path integrals
• From covariant to canonical formulations of discrete gravity
• Time evolution as refining, coarse graining and entangling
• Loop and spin foam quantum gravity: a brief guide for beginners
• Coarse graining flow of spin foam intertwiners
• Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity
• Can chaos be observed in quantum gravity?
• Implementing causality in the spin foam quantum geometry
• 3+1 spinfoam model of quantum gravity with spacelike and timelike components
• Spin Foam Models of Riemannian Quantum Gravity
• On the regularization of the constraints algebra of Quantum Gravity in 2+1 dimensions with non-vanishing cosmological constant
• Critical Overview of Loops and Foams
• The century of the incomplete revolution: searching for general relativistic quantum field theory
• Bubble divergences and gauge symmetries in spin foams
• The Feynman propagator for spin foam quantum gravity
• The cubic matrix model and a duality between strings and loops
• Causality and matter propagation in 3d spin foam quantum gravity
• Positivity of Spin Foam Amplitudes
• Timelike surfaces in Lorentz covariant loop gravity and spin foam models
• From 3-geometry transition amplitudes to graviton states
• Addendum: EPRL/FK Asymptotics and the Flatness Problem
• Extended matter coupled to BF theory
• Quantization of systems with temporally varying discretization II: Local evolution moves
• A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
• Radiation from quantum weakly dynamical horizons in LQG
• Spin-Foam Models and the Physical Scalar Product
• Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
• Solving the Problem of Time in Mini-superspace: Measurement of Dirac Observables
• Topological excitations around the vacuum of quantum gravity I: The symmetries of the vacuum
• Topological lattice field theories from intertwiner dynamics
• Causality in Spin Foam Models
• Spin-foam model for gravity coupled to massless scalar field
• Relating Covariant and Canonical Approaches to Triangulated Models of Quantum Gravity
• Timelike twisted geometries
• Chaos, Dirac observables and constraint quantization
• The accidental flatness constraint does not mean a wrong classical limit
• Spinfoams: Foundations
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Reparameterization invariants for anisotropic Bianchi I cosmology with a massless scalar source
• Canonical ``Loop'' Quantum Gravity and Spin Foam Models
• 2+1 gravity with positive cosmological constant in LQG: a proposal for the physical state
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
• String theory in a vertex operator representation: a simple model for testing loop quantum gravity
• A review on Loop Quantum Gravity
• Relating Spin Foams and Canonical Quantum Gravity: A Discrete Step Evolution Formulation of Spin Foams
• Quantum Cauchy Surfaces in Canonical Quantum Gravity
• Emergence of scalar matter from spinfoam model
• Emergence of General Relativity from Loop Quantum Gravity: A Summary
• Quantum Reference Frames via Transition Amplitudes in Timeless Quantum Gravity
• Spin Foam Models of Gravity and BF Theory as evolution of Spin Networks
• The relation between Geometry and Matter in classical and quantum Gravity and Cosmology