Loop quantum gravity: an outside view

Abstract

We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a crucial test of quantum space-time covariance, and thereby of the consistency, of the theory. Special attention is paid to the appearance of a large number of ambiguities, in particular in the formulation of the Hamiltonian constraint. Developing suitable approximation methods to establish a connection with classical gravity on the one hand, and with the physics of elementary particles on the other, remains a major challenge.

57 pages, 11 figures; v2: substantially revised, references added, resubmitted to Class. Quant. Grav.; v3: further substantial improvements; v4: small changes, final version to appear in Class. Quant. Grav

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• Diffeomorphism covariant representations of the holonomy-flux star-algebra
• Yang-Mills analogues of the Immirzi ambiguity
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• Diffeomorphisms as Symplectomorphisms in History Phase Space: Bosonic String Model
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• The regularized BRST Jacobian of pure Yang-Mills theory
• Long range correlations in quantum gravity
• DDF and Pohlmeyer invariants of (super)string

Cited by in corpus (104)

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• Loop Quantum Gravity: An Inside View
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• Covariance in models of loop quantum gravity: Spherical symmetry
• Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity
• Anomaly-free cosmological perturbations in effective canonical quantum gravity
• How Far Are We from the Quantum Theory of Gravity?
• Anomaly-free perturbations with inverse-volume and holonomy corrections in Loop Quantum Cosmology
• Limit on Lorentz and CPT violation of the bound Neutron Using a Free Precession 3He/129Xe co-magnetometer
• Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
• Classical and Quantum Features of the Mixmaster Singularity
• Canonical Gravity with Fermions
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• Fock representation of gravitational boundary modes and the discreteness of the area spectrum
• Primordial scalar power spectrum from the Euclidean Big Bounce
• Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I
• Anomaly-free vector perturbations with holonomy corrections in loop quantum cosmology
• Spherically symmetric canonical quantum gravity
• Inhomogeneities, loop quantum gravity corrections, constraint algebra and general covariance
• Critical Overview of Loops and Foams
• The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics
• Constraint algebra in LQG reloaded : Toy model of an Abelian gauge theory - II Spatial Diffeomorphisms
• Seeking the Loop Quantum Gravity Barbero-Immirzi Parameter and Field in 4D, $\mathcal{N}$ = 1 Supergravity
• High-Energy Scatterings in Infinite-Derivative Field Theory and Ghost-Free Gravity
• Diffeomorphism Invariance in the Hamiltonian formulation of General Relativity
• Dirac's discrete hypersurface deformation algebras
• Quantum Gravity as an Information Network: Self-Organization of a 4D Universe
• Black Hole Solutions for Scale Dependent Couplings: The de Sitter and the Reissner-Nordström Case
• Observations in Quantum Cosmology
• The Born-Oppenheimer Method, Quantum Gravity and Matter
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• The constraints of post-quantum classical gravity
• Constraints and the E10 Coset Model
• Minimal Scales from an Extended Hilbert Space
• Generalised Boundary Terms for Higher Derivative Theories of Gravity
• Some Aspects of Virtual Black Holes
• Emerging singularities in the bouncing loop cosmology
• Study of the Inflationary Spectrum in the Presence of Quantum Gravity Corrections
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• Turning big bang into big bounce: II. Quantum dynamics
• Brane-world Quantum Gravity
• Discreteness of Space from GUP in Strong Gravitational Fields
• On the UV dimensions of Loop Quantum Gravity
• Quantum Gravity: the view from particle physics
• Random Holographic "Large Worlds" with Emergent Dimensions
• Constraining the loop quantum gravity parameter space from phenomenology
• Conformal boundary conditions, loop gravity and the continuum
• Polymer quantization of the Einstein-Rosen wormhole throat
• Generalized Ashtekar variables for Palatini f(R) models
• The Raychaudhuri equation for a quantized timelike geodesic congruence
• The Hamiltonian of Einstein affine-metric formulation of General Relativity
• Singularity resolution from polymer quantum matter
• Testing and selection of cosmological models with $(1+z{)}^6$ corrections
• On Spectral Triples in Quantum Gravity I
• Rainbow-like Black Hole metric from Loop Quantum Gravity
• Effective Field Theory of Loop Quantum Cosmology
• What kind of science is cosmology?
• Quantum no-singularity theorem from geometric flows
• Quantum Geometry and its Implications for Black Holes
• General Formalism of the Quantum Equivalence Principle
• Dynamic coarse-graining approach to quantum field theory
• Is it time to rethink quantum gravity?
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• Large classical universes emerging from quantum cosmology
• Wheeler's It from Bit Proposal in Loop Quantum Gravity
• Probing the cosmological singularity with a particle
• Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
• Loop quantum cosmology and the Wheeler-De Witt equation
• Symmetric black-to-white hole solutions with a cosmological constant
• Absorption cross section in gravity's rainbow from confluent Heun equation
• Two-Connection Renormalization and Nonholonomic Gauge Models of Einstein Gravity
• Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing
• A Variational Formulation of Symplectic Noncommutative Mechanics
• Graphs (networks) with golden spectral ratio
• "Clumpiness" Mixing in Complex Networks
• Phase Transition in Loop Quantum Gravity
• Quantum Holonomy Theory
• Properties of the Hamiltonian Renormalisation and its application to quantum mechanics on the circle
• Classical corrections to black hole entropy in $d$ dimensions: a rear window to quantum gravity?
• Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections
• Virtual Black Holes from Generalized Uncertainty Principle and Proton Decay
• Critical Space-Time Networks and Geometric Phase Transitions from Frustrated Edge Antiferromagnetism
• Is the diagonal case a general picture for Loop Quantum Cosmology?
• A discrete, unitary, causal theory of quantum gravity
• Dynamics and the Emergence of Geometry in an Information Mesh
• Matter in Loop Quantum Gravity
• A Bohr's Semiclassical Model of the Black Hole Thermodynamics
• The role of spatial curvature in constraining the Universe anisotropies across a Big Bounce
• Quantum variational solving of the Wheeler-DeWitt equation
• Asymptotic Flatness and Quantum Geometry
• Emergence of General Relativity from Loop Quantum Gravity: A Summary
• On Special Re-quantization of a Black Hole
• Cosmological bounce and the cosmological constant problem
• The ADM papers and part of their modern legacy: loop quantum gravity
• Cosmological implications of the hydrodynamical phase of group field theory
• Canonical Gravity in Degenerate Limit
• Test of Quantum Gravity in Optical Magnetometers
• Wigner functions, Fresnel optics, and symplectic connections on phase space
• The canonical formulation of E${}_{6(6)}$ exceptional field theory
• Complete loop quantization of a dimension 1+2 Lorentzian gravity theory