The Spin Foam Approach to Quantum Gravity

Abstract

This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of the 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.

To appear in Living Reviews in Relativity

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• Continuous point symmetries in Group Field Theories
• Discrete gravity as a topological field theory with light-like curvature defects
• Spin-foam model for gravity coupled to massless scalar field
• On the volume simplicity constraint in the EPRL spin foam model
• Canonical analysis of Holst action without second-class constraints
• Suppression of spacetime singularities in quantum gravity
• Pauli-Fierz mass term in modified Plebanski gravity
• Hawking radiation in the kappa-spacetime
• Coherent Quantum Dynamics: What Fluctuations Can Tell
• Understanding truncated non-commutative geometries through computer simulations
• Area Law from Loop Quantum Gravity
• Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases
• Holonomy-flux spinfoam amplitude
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• Noncommutative gravity with self-dual variables
• Canonical formulation of Poincare BFCG theory and its quantization
• Lorentzian quantum cosmology from effective spin foams
• Corner symmetry and quantum geometry
• Entanglement entropy and correlations in loop quantum gravity
• Loop Quantum Gravity's Boundary Maps
• Holographic description of boundary gravitons in (3+1) dimensions
• Thermal quantum spacetime
• Timelike twisted geometries
• Numerical evaluation of spin foam amplitudes beyond simplices
• Radiative corrections to the Lorentzian EPRL spin foam propagator
• Non-commutative Fourier transform for the Lorentz group via the Duflo map
• From Noncommutative Geometry to Random Matrix Theory
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Quantum gravity in three dimensions, Witten spinors and the quantisation of length
• Hopf link volume simplicity constraints in spin foam models
• Visions in Quantum Gravity
• Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations
• The closure constraint for the hyperbolic tetrahedron as a Bianchi identity
• Alternative derivation of Krasnov's action for general relativity
• Hamiltonian analysis of unimodular gravity and its quantization in the connection representation
• Spinfoams: Foundations
• Coherent 3j-symbol representation for the loop quantum gravity intertwiner space
• Experimental Simulation of Loop Quantum Gravity on a Photonic Chip
• Time-space duality in 2D quantum gravity
• Modification of the mean free path of very high energy photons due to a relativistic deformed kinematics
• Area-metric gravity revisited
• Towards anisotropic cosmology in group field theory
• Deformation of the EPRL spin foam model by a cosmological constant
• Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Hamiltonian analysis of the BFCG formulation of General Relativity
• Spikes and spines in 4D Lorentzian simplicial quantum gravity
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• The thermodynamics of quantum spacetime histories
• The Barrett-Crane model: asymptotic measure factor
• Influence of Quantum Correction on Kerr Black Hole in Effective Loop Quantum Gravity via Shadows and EHT Results
• Three-dimensional Background Field Gravity: A Hamilton-Jacobi analysis
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
• Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• Group quantization of the black hole minisuperspace
• Path integral renormalisation in loop quantum cosmology
• $SU(1,1)$ Barbero-like variables derived from Holst action
• Path integral and conformal instability in nonlocal quantum gravity
• Poincare-Plebanski formulation of GR and dual simplicity constraints
• Scalar Cosmological Perturbations from Quantum Gravitational Entanglement
• Trace-free Einstein gravity as a constrained bigravity theory
• Properties of the Hamiltonian Renormalisation and its application to quantum mechanics on the circle
• A one-dimensional action for simplicial gravity in three dimensions
• Diffeomorphism-invariant action principles for trace-free Einstein gravity
• Stable coherent states
• Network Gravity
• The Quantum Gravity Disk: Discrete Current Algebra
• Holographic relations in loop quantum gravity
• Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory
• Deformations of GR, Geometrodynamics and Reality Conditions
• Barbero's formulation from a $BF$-type action with the Immirzi parameter
• Towards self dual Loop Quantum Gravity
• Twistor representation of Jackiw-Teitelboim gravity
• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
• Toward matter dynamics in spin foam quantum gravity
• Black Hole Remnants from Dynamical Dimensional Reduction?
• Intertwiner Entanglement Excitation and Holonomy Operator
• Energetics of the Quantum Graphity Universe
• Spinfoam cosmology with the proper vertex amplitude
• Stochastic dynamics for Group Field Theories
• The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
• Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
• Loop Quantum Gravity effects on electromagnetic properties of charged leptons
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
• Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
• Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
• Propagators in the Correlated Worldline Theory of Quantum Gravity
• Generalised Gaussian states in group field theory and $\mathfrak{su}(1,1)$ quantum cosmology
• Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data
• Curvature effects in the spectral dimension of spin foams
• A Monte Carlo algorithm for spin foam intertwiners
• Loop quantum gravity, twistors, and some perspectives on the problem of time
• A Wick rotation for EPRL spin foam models
• Regarding the `Hole Argument' and the `Problem of Time'
• Dynamics in canonical models of loop quantum gravity
• Multisymplectic effective General Boundary Field Theory
• Nakanishi-Kugo-Ojima quantization of general relativity in Heisenberg picture
• Non-commutative quantum geometric data in group field theories
• Geometry from local flatness in Lorentzian spin foam theories
• Causal structure in spin-foams
• Relating spin-foam to canonical loop quantum gravity by graphical calculus
• Deformed Heisenberg charges in three-dimensional gravity
• Spin foams
• Quantum gravity and gravitational-wave astronomy
• Relational dynamics and Page-Wootters formalism in group field theory
• Modified Graviton Dynamics From Spin Foams: The Area Regge Action
• On the discrete version of the Schwarzschild problem
• Field redefinitions and Plebanski formalism for GR
• Covariant effective spacetimes of spherically symmetric electrovacuum with a cosmological constant
• Spin foam propagator: A new perspective to include a cosmological constant
• Can quantum gravity be both consistent and complete?
• $\Psi$-Epistemic Quantum Cosmology?
• Plebanski-like action for general relativity and anti-self-dual gravity
• Fractional Einstein field equations in $2+1$ dimensional spacetime
• A simpler way of imposing simplicity constraints
• On the discrete version of the black hole solution
• Curvature from multipartite entanglement in quantum gravity states
• Spherically-symmetric geometries in a matter reference frame as quantum gravity condensates
• From area metric backgrounds to the cosmological constant and corrections to the Polyakov action
• Polysymplectic formulation for BF gravity with Immirzi parameter
• Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme
• GEMs and amplitude bounds in the colored Boulatov model
• Classical and Quantum Polyhedra
• Localization and diffusion in polymer quantum field theory
• Off-shell Noether currents and potentials for first-order general relativity
• The Autodidactic Universe
• Hilbert space formalisms for group field theory
• Effective Actions for Regge Piecewise Flat Quantum Gravity
• New first order Lagrangian for General Relativity
• Studying the EPRL spinfoam self-energy
• Canonical analysis with no second-class constraints of $BF$ gravity with Immirzi parameter
• A Model of Spinfoam Coupled with an Environment
• Constraint Analysis of Two-Dimensional Quadratic Gravity from BF Theory
• Weak gravitational interaction of fermions: quantum viewpoint
• Quantum fate of timelike naked singularity with scalar hair
• Finiteness of quantum gravity with matter on a PL spacetime
• A look at area Regge calculus
• Unimodular Plebański Gravity
• Aspects of quantum gravity
• Is the local linearity of space-time inherited from the linearity of probabilities?
• Combinatorial Cell Complexes: Duality, reconstruction and causal cobordisms
• Causal structure and topology change in (2+1)-dimensional simplicial gravity
• Evidence for Planck Luminosity Bound in Quantum Gravity
• Cosmological Constant in a Quantum Gravity Theory for a Piecewise-linear Spacetime
• Fiber bundle structure in Ashtekar-Barbero-Immirzi formulation of General Relativity
• Trace-free Einstein gravity as two interacting constrained $BF$ theories
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Semiclassical states in quantum gravity: Curvature associated to a Voronoi graph
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Light ray fluctuation and lattice refinement of simplicial quantum gravity
• Monte Carlo simulation of cosmologies with dust
• On the discrete version of the Kerr-Newman solution
• Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
• Polyhedra in spacetime from null vectors
• Natural discrete differential calculus in physics
• A spin foam framework for the black-to-white hole transition
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Lorentzian quantum gravity via Pachner moves: one-loop evaluation
• Cosmological implications of the hydrodynamical phase of group field theory
• Particles as superoscillations of spacetime with a nonlocal metric?
• A discretization of Holst's action for general relativity
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
• Transition probability spaces in loop quantum gravity
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality
• Loop quantum gravity with optimal control path integral, and application to black hole tunneling
• 3D Quantum Gravity from Holomorphic Blocks
• Discrete Hamiltonian for General Relativity
• World quantum gravity: Quantum test objects and Synge's world function
• Hessian in the spinfoam models with cosmological constant
• Relational Quadrilateralland. II. The Quantum Theory
• Kant and Quantum Gravity
• Conceptual and Geometric Foundations for a Teleparallel Approach to Quantum Gravity
• Ergodic Concepts for a Self-Organizing Trivalent Spin Network: A Path to $(2+1)$-dimensional Black Hole Entropy
• Hidden Symmetries in Gravity : Black holes and other minisuperspaces
• Canonical analysis of $BF$ gravity in $n$ dimensions
• A quantum theory of gravity
• Quantum Spacetime Imprints: The 24-Cell, Standard Model Symmetry and Its Flavor Mixing
• Canonical description of Exotic General Massive Gravity
• Knot invariants and indefinite causal order
• Flat spin connections in the Teleparallel equivalent of General Relativity
• Endeavours in Discrete Lorentzian Geometry; A thesis in five papers
• Nonlocal correlations for semiclassical states in loop quantum gravity
• A topological-like gravity model in a four dimensional space-time
• Quantum mechanics as an approximated model: A geometrodynamical approach
• Group field theories generating polyhedral complexes
• Fate of chiral symmetry in Riemann-Cartan geometry