Path integral representation of spin foam models of 4d gravity

Abstract

We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= gamma < 1, the states can be restricted to SU(2) spin networks.

29 pages, 6 figures

References in corpus (25)

• LQG vertex with finite Immirzi parameter
• Spin Foam Models for Quantum Gravity
• Relativistic spin networks and quantum gravity
• A new spinfoam vertex for quantum gravity
• Spin Foam Models
• The loop-quantum-gravity vertex-amplitude
• Group Field Theory: An overview
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• Flipped spinfoam vertex and loop gravity
• Spacetime as a Feynman diagram: the connection formulation
• Three dimensional loop quantum gravity: physical scalar product and spin foam models
• Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
• A "general boundary" formulation for quantum mechanics and quantum gravity
• SU(2) Loop Quantum Gravity seen from Covariant Theory
• SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter
• Particle scattering in loop quantum gravity
• On choice of connection in loop quantum gravity
• Lorentzian LQG vertex amplitude
• Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity
• Area spectrum in Lorentz covariant loop gravity
• The dual of pure non-Abelian lattice gauge theory as a spin foam model
• Barrett-Crane spin foam model from generalized BF-type action for gravity
• Hilbert space structure of covariant loop quantum gravity
• Coherent states, constraint classes, and area operators in the new spin-foam models

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• Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
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• Spin foam models for quantum gravity from lattice path integrals
• Quantum geometry from phase space reduction
• Quantum deformation of two four-dimensional spin foam models
• (Broken) Gauge Symmetries and Constraints in Regge Calculus
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• Simplicity in simplicial phase space
• Lorentz covariance of loop quantum gravity
• Holomorphic Factorization for a Quantum Tetrahedron
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
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• From lattice BF gauge theory to area-angle Regge calculus
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• A proposed proper EPRL vertex amplitude
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• A Lagrangian approach to the Barrett-Crane spin foam model
• The Holst Spin Foam Model via Cubulations
• Discrete Symmetries in Covariant LQG
• Spin foams with timelike surfaces
• Emergence of gravity from spinfoams
• Euclidean three-point function in loop and perturbative gravity
• Asymptotics of 4d spin foam models
• Numerical computations of next-to-leading order corrections in spinfoam large-$j$ asymptotics
• EPRL/FK Asymptotics and the Flatness Problem
• Sub-leading asymptotic behaviour of area correlations in the Barrett-Crane model
• Analytic Continuation of Spin foam Models
• Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases
• Group field theory and simplicial quantum gravity
• Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-${\Delta }_3$ complex
• Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions
• Encoding simplicial quantum geometry in group field theories
• A finiteness bound for the EPRL/FK spin foam model
• The thermodynamics of quantum spacetime histories
• Second-order amplitudes in loop quantum gravity
• Evaluation of new spin foam vertex amplitudes
• Cosmological Plebanski theory
• Transition probability spaces in loop quantum gravity
• Commuting Simplicity and Closure Constraints for 4D Spin Foam Models
• Attributing sense to some integrals in Regge calculus