Discrete approaches to quantum gravity in four dimensions

Abstract

The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.

33 pages, invited contribution to Living Reviews in Relativity; the author welcomes any comments and suggestions

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Cited by in corpus (144)

• Minimal Length Scale Scenarios for Quantum Gravity
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• Loop Quantum Cosmology
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• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• A non-perturbative Lorentzian path integral for gravity
• Quantum cosmology: a review
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Gravity and the Quantum
• The Universe from Scratch
• Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
• Geometry and field theory in multi-fractional spacetime
• Dimension and Dimensional Reduction in Quantum Gravity
• Area-angle variables for general relativity
• Non-perturbative 3d Lorentzian Quantum Gravity
• Diffeomorphisms in group field theories
• Quantum Spin Dynamics (QSD) : VII. Symplectic Structures and Continuum Lattice Formulations of Gauge Field Theories
• Tensorial methods and renormalization in Group Field Theories
• Coarse graining methods for spin net and spin foam models
• From the discrete to the continuous - towards a cylindrically consistent dynamics
• Second- and First-Order Phase Transitions in CDT
• Perfect discretization of reparametrization invariant path integrals
• Phase Transition in Dually Weighted Colored Tensor Models
• Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations
• Discrete Lorentzian Quantum Gravity
• Canonical quantization of general relativity in discrete space-times
• From covariant to canonical formulations of discrete gravity
• Path integral measure and triangulation independence in discrete gravity
• Canonical simplicial gravity
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
• Loop and spin foam quantum gravity: a brief guide for beginners
• Time evolution as refining, coarse graining and entangling
• Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds
• The Double Scaling Limit in Arbitrary Dimensions: A Toy Model
• Coarse graining free theories with gauge symmetries: the linearized case
• A geometric discretisation scheme applied to the Abelian Chern-Simons theory
• Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?
• Evidence for a Phase Transition in 2D Causal Set Quantum Gravity
• Quantization of Midisuperspace Models
• Towards classical geometrodynamics from Group Field Theory hydrodynamics
• Group field theory condensate cosmology: An appetizer
• From lattice BF gauge theory to area-angle Regge calculus
• Discrete Riemannian Geometry
• Introducing Quantum Ricci Curvature
• Spacetime foam: a review
• Ollivier-Ricci curvature convergence in random geometric graphs
• (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
• Introduction to Loop Quantum Gravity
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• Laplacians on discrete and quantum geometries
• From spin foams to area metric dynamics to gravitons
• Lorentzian quantum cosmology goes simplicial
• Torsion in quantum field theory through time-loops on Dirac materials
• Discrete quantum gravity: applications to cosmology
• Semiclassical regime of Regge calculus and spin foams
• Theory and Phenomenology of Spacetime Defects
• A discrete history of the Lorentzian path integral
• Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations
• The Complete Barrett-Crane Model and its Causal Structure
• Kahler-Einstein metrics emerging from free fermions and statistical mechanics
• Quantum Reference Frames at the Boundary of Spacetime
• Is the spin connection confined or condensed?
• Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
• Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
• Semiclassical Quantum Gravity: Statistics of Combinatorial Riemannian Geometries
• Detailed discussions and calculations of quantum Regge calculus of Einstein-Cartan theory
• Quantum Regge Calculus of Einstein-Cartan theory
• Consistent discretization and canonical classical and quantum Regge calculus
• The phase and critical point of quantum Einstein-Cartan gravity
• A first look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• Spontaneous Dimensional Reduction?
• Singularity resolution from polymer quantum matter
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Discrete gravity as a topological field theory with light-like curvature defects
• Graphene and Black Holes: novel materials to reach the unreachable
• Unexpected Spin-Off from Quantum Gravity
• Understanding truncated non-commutative geometries through computer simulations
• Torsion at different scales: from materials to the Universe
• Area expectation values in quantum area Regge calculus
• What kind of science is cosmology?
• Curvature profiles for quantum gravity
• Gravitational Corrections to the Energy-Levels of a Hydrogen Atom
• Semiclassical Quantum Gravity: Obtaining Manifolds from Graphs
• Dirac Operators and the Calculation of the Connes Metric on arbitrary (Infinite) Graphs
• Quantum Flatness in Two-Dimensional CDT Quantum Gravity
• Lattice quantum gravity - an update
• Emergent matter from 3d generalised group field theories
• Quantum widening of CDT universe
• A causal perspective on random geometry
• Two-body decays in deformed relativity
• Time-space duality in 2D quantum gravity
• Being, Becoming and the Undivided Universe: A Dialogue between Relational Blockworld and the Implicate Order Concerning the Unification of Relativity and Quantum Theory
• On the non-perturbative graviton propagator
• Hamiltonian Renormalisation V: Free Vector Bosons
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• Appearing Out of Nowhere: The Emergence of Spacetime in Quantum Gravity
• Emergence of gravity from interacting simplices
• Surface embedding, topology and dualization for spin networks
• General Ether Theory
• Scalar Cosmological Perturbations from Quantum Gravitational Entanglement
• Perfect discretizations as a gateway to one-loop partition functions for 4D gravity
• A discrete nonetheless remarkable brick in de Sitter: the "massless minimally coupled field"
• Finite group discretization of Yang-Mills and Einstein actions
• Background-Independent Composite Gravity
• Spherical symmetry in a dark energy permeated space-time
• Gravitational Collapse via Wheeler-DeWitt Equation
• Sums over geometries and improvements on the mean field approximation
• Teleparallel gravity on the lattice
• Approximate Killing symmetries in non-perturbative quantum gravity
• Dynamical Evolution in Noncommutative Discrete Phase Space and the Derivation of Classical Kinetic Equations
• Light ray fluctuations in simplicial quantum gravity
• Classicity from Entangled Ensemble States of Knotted Spin Networks. A Conceptual Approach
• A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• Analytic Results in 2D Causal Dynamical Triangulations: A Review
• Aspects of quantum gravity
• Quantum Perturbative Approach to Discrete Redshift
• Modelling gravity on a hyper-cubic lattice
• Riemannian Geometry of Bicovariant Group Lattices
• Light ray fluctuation and lattice refinement of simplicial quantum gravity
• Quantum Gravity from Simplices: Analytical Investigations of Causal Dynamical Triangulations
• Strict renormalizability as a paradigm for fundamental physics
• Background Independence and Quantum Causal Structure
• Semiclassical states in quantum gravity: Curvature associated to a Voronoi graph
• On Some Information-geometric aspects of Hawking radiation
• A No-go theorem for Poincaré-invariant networks
• A Metric Theory of Gravity with Condensed Matter Interpretation
• Local Space-Time Curvature Effects on Quantum Orbital Angular Momentum
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Discrete Gravity with Local Lorentz Invariance
• Time-loops to spot torsion on bidimensional Dirac materials with dislocations
• Lorentzian quantum gravity via Pachner moves: one-loop evaluation
• World quantum gravity: Quantum test objects and Synge's world function
• Discrete Hamiltonian evolution and quantum gravity
• Gauge Invariance from a Graphical Self-Consistency Criterion
• Five Dimensional Dynamical Triangulations
• Analysis of the Semiclassical Solution of CDT
• Discrete canonical analysis of three dimensional gravity with cosmological constant
• Combinatorial Dark Energy
• Causal Space-Times on a Null Lattice
• Time-covariant Schrödinger equation and invariant decay probability: The $\Lambda$-Kantowski-Sachs universe
• Physical States and Transition Amplitudes in Piecewise Flat Quantum Gravity
• An Adynamical, Graphical Approach to Quantum Gravity and Unification