The loop-quantum-gravity vertex-amplitude

Abstract

Spinfoam theories are hoped to provide the dynamics of non-perturbative loop quantum gravity. But a number of their features remain elusive. The best studied one -the euclidean Barrett-Crane model- does not have the boundary state space needed for this, and there are recent indications that, consequently, it may fail to yield the correct low-energy $n$-point functions. These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way certain second class constraints are imposed, arguably incorrectly, strongly. We present an alternative model, that can be derived as a bona fide quantization of a Regge discretization of euclidean general relativity, and where the constraints are imposed weakly. Its state space is a natural subspace of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network space. The model provides a long sought SO(4)-covariant vertex amplitude for loop quantum gravity.

6pages

References in corpus (32)

• Discreteness of area and volume in quantum gravity
• Quantum Theory of Gravity I: Area Operators
• Quantum Spin Dynamics (QSD)
• Spin Foam Models for Quantum Gravity
• Relativistic spin networks and quantum gravity
• Weaving a classical geometry with quantum threads
• Spin Foam Models
• Group Field Theory: An overview
• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• Graviton propagator from background-independent quantum 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
• so(4) Plebanski Action and Relativistic Spin Foam Model
• Multipole Moments of Isolated Horizons
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• SU(2) Loop Quantum Gravity seen from Covariant Theory
• The basis of the Ponzano-Regge-Turaev-Viro-Ooguri model is the loop representation basis
• A spin foam model without bubble divergences
• Spin foam model for Lorentzian General Relativity
• Quantum Spin Dynamics VIII. The Master Constraint
• Hamiltonian Analysis of Plebanski Theory
• Particle scattering in loop quantum gravity
• On choice of connection in loop quantum gravity
• Group Integral Techniques for the Spinfoam Graviton Propagator
• Finiteness of a spinfoam model for euclidean quantum general relativity
• A left-handed simplicial action for euclidean general relativity
• On relativistic spin network vertices
• Towards the graviton from spinfoams: higher order corrections in the 3d toy model
• Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity
• Spin Foam Models of Riemannian Quantum Gravity
• Towards the graviton from spinfoams: the 3d toy model

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