Loop quantum gravity: the first twenty five years

Abstract

This is a review paper invited by the journal "Classical ad Quantum Gravity" for a "Cluster Issue" on approaches to quantum gravity. I give a synthetic presentation of loop gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits.

24 pages, 3 figures

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• Quantum Transfiguration of Kruskal Black Holes
• Cosmological and Solar System Consequences of f(R,T) Gravity Models
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• Relational Observables in Gravity: a Review
• Effects of quantum gravity on black holes
• Small black/white hole stability and dark matter
• Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
• $BF$ gravity
• Quantum Gravity: A Brief History of Ideas and Some Prospects
• Bohr-Sommerfeld Quantization of Space
• Loop Quantum Gravity
• Regge gravity from spinfoams
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint
• Inconstant Planck's constant
• Curvature in spinfoams
• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• A critical look at strings
• Manifestly Lorentz-covariant variables for the phase space of general relativity
• Effective cosmological constant induced by stochastic fluctuations of Newton's constant
• From 3D topological quantum field theories to 4D models with defects
• Wilson loops in CDT quantum gravity
• Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation
• Canonical analysis of Holst action without second-class constraints
• Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity
• Flowing in discrete gravity models and Ward identities: A review
• Nonlocal Entanglement and Directional Correlations of Primordial Perturbations on the Inflationary Horizon
• Two-Point Functions on Deformed Spacetime
• The Barbero-Immirzi Parameter: An Enigmatic Parameter of Loop Quantum Gravity
• Quantization of time and the big bang via scale-invariant loop gravity
• $SU(1,1)$ Barbero-like variables derived from Holst action
• Revisiting the solution of the second-class constraints of the Holst action
• Physics in non-fixed spatial dimensions via random networks
• A "Helium Atom" of Space: Dynamical Instability of the Isochoric Pentahedron
• Quantum Gravity from the Composition of Spacetime Constructed through Generalised Proper Time
• Two-spinor geometry and gauge freedom
• A scale at 10 MeV, gravitational topological vacuum, and large extra dimensions
• The Structure of Matter in Spacetime from the Substructure of Time
• Fix Immirzi parameter by quasinormal modes in four and higher spacetime dimensions
• Quantum Entanglement Dynamics of Spacetime and Matter
• Homogeneous-isotropic sector of loop quantum gravity: new approach
• Properties of the Rovelli-Smolin-DePietri volume operator in the spaces of monochromatic intertwiners
• Synopsis of a Unified Theory for All Forces and Matter
• Universal Entanglement and an Information-Complete Quantum Theory
• FRW cosmology of the generalized model of LQG
• Categorical Quantum Volume Operator
• Is torsion needed in a theory of gravity? A reappraisal
• The Entropic Dynamics of Relativistic Quantum Fields in Curved Space-time