Fundamental Structure of Loop Quantum Gravity

Abstract

In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of kinematical Ashtekar-Isham-Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background independent quantum gauge theories. There is no divergence within this background independent and diffeomorphism invariant quantization programme of matter coupled to gravity.

82 pages, no figures, revised version accepted for publication in IJMPD

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• Semiclassical States for Constrained Systems
• Spin Networks for Non-Compact Groups
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• Initial Conditions for a Universe
• Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories
• Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models
• Genericness of inflation in isotropic loop quantum cosmology
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• Semiclassical zero temperature black holes in spherically reduced theories
• Hilbert space built over connections with a non-compact structure group
• Quantum Riemannian Geometry and Black Holes
• Quantization of static space-times
• Semi-classical States in Homogeneous Loop Quantum Cosmology

Cited by in corpus (202)

• Introduction to Loop Quantum Cosmology
• Alternative quantization of the Hamiltonian in loop quantum cosmology II: Including the Lorentz term
• Spin-Foams for All Loop Quantum Gravity
• Shadow and stability of quantum-corrected black holes
• 4-dimensional Spin-foam Model with Quantum Lorentz Group
• SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
• Extension of loop quantum gravity to $f(R)$ theories
• Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
• Lorentzian spinfoam propagator
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
• New length operator for loop quantum gravity
• Cosmological Constant in LQG Vertex Amplitude
• Operator Spin Foam Models
• Generalized Spinfoams
• Loop quantum Schwarzschild interior and black hole remnant
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
• Loop quantum $f(R)$ theories
• Nonperturbative Loop Quantization of Scalar-Tensor Theories of Gravity
• New scalar constraint operator for loop quantum gravity
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Effective Scenario of Loop Quantum Cosmology
• Hamiltonian operator for loop quantum gravity coupled to a scalar field
• Quasinormal frequencies of self-dual black holes
• Primordial black holes in loop quantum cosmology: The effect on the threshold
• Group field theory for quantum gravity minimally coupled to a scalar field
• Derivations of group rings
• Quantum-corrected scattering and absorption of a Schwarzschild black hole with GUP
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Master Constraint Operator in Loop Quantum Gravity
• Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
• Loop quantum deparametrized Schwarzschild interior and discrete black hole mass
• On Spinfoam Models in Large Spin Regime
• Semiclassical Analysis of Spinfoam Model with a Small Barbero-Immirzi Parameter
• Path Integral Representation of Lorentzian Spinfoam Model, Asymptotics, and Simplicial Geometries
• A curvature operator for LQG
• Asymptotic analysis of spin foam amplitude with timelike triangles
• A symmetric scalar constraint for loop quantum gravity
• Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
• Loop quantum black hole
• New Hamiltonian constraint operator for loop quantum gravity
• A comparison between Jordan and Einstein frames of Brans-Dicke gravity a la loop quantum cosmology
• Loop quantum Brans-Dicke cosmology
• Coherent intertwiner solution of simplicity constraint in all dimensional loop quantum gravity
• Improved ($\bar{\mu }$-Scheme) Effective Dynamics of Full Loop Quantum Gravity
• Dark Energy Interacting with Dark Matter in Classical Einstein and Loop Quantum Cosmology
• Bouncing evolution in a model of loop quantum gravity
• Extended Phase Space Analysis of Interacting Dark Energy Models in Loop Quantum Cosmology
• The EPRL intertwiners and corrected partition function
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Effective four-dimensional loop quantum black hole with a cosmological constant
• Time evolution in deparametrized models of loop quantum gravity
• Quantum Spacetime on a Quantum Simulator
• New volume and inverse volume operators for loop quantum gravity
• BF Theory Explanation of the Entropy for Non-rotating Isolated Horizons
• Numerical computations of next-to-leading order corrections in spinfoam large-$j$ asymptotics
• The volume operator in covariant quantum gravity
• Emergent 4-dimensional linearized gravity from spin foam model
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• The Lensing Effect of Quantum-Corrected Black Hole and Parameter Constraints from EHT Observations
• Evolution of Primordial Black Holes in Loop Quantum Gravity
• Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics
• Thermal quantum gravity condensates in group field theory cosmology
• Loop Quantum Brans-Dicke Theory
• Reduced Phase Space Quantization of Black Holes: Path Integrals, and Effective Dynamics
• Pre-inflationary dynamics of Starobinsky inflation and its generization in Loop Quantum Brans-Dicke Cosmology
• Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology
• The effective dynamics of loop quantum $R^2$ cosmology
• Shadows and optical appearance of quantum-corrected black holes illuminated by static thin accretions
• Dynamics of Scalar Field in Polymer-like Representation
• Entropy of black holes with arbitrary shapes in loop quantum gravity
• Analytic Continuation of Spin foam Models
• General geometric operators in all dimensional loop quantum gravity
• Periodic orbits and gravitational waveforms in quantum-corrected black hole spacetimes
• Higher dimensional Loop Quantum Cosmology
• Loop Quantum Gravity on Dynamical Lattice and Improved Cosmological Effective Dynamics with Inflaton
• Higher-dimensional quantum Oppenheimer-Snyder model
• Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity
• Polytopes in all dimensional loop quantum gravity
• Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology
• Feynman diagrammatic approach to spin foams
• Anomaly freedom in perturbative models of Euclidean loop quantum gravity
• Efficient Simulation of Loop Quantum Gravity -- A Scalable Linear-Optical Approach
• Thermal representations in group field theory: squeezed vacua and quantum gravity condensates
• Finite-distance gravitational deflection of massive particles by a rotating black hole in loop quantum gravity
• Anyonic statistics and large horizon diffeomorphisms for Loop Quantum Gravity Black Holes
• On Spinfoams Near a Classical Curvature Singularity
• Manifestly Gauge-Invariant Cosmological Perturbation Theory from Full Loop Quantum Gravity
• Coherent State Functional Integrals in Quantum Cosmology
• Perelomov type coherent states of SO(D + 1) in all dimensional loop quantum gravity
• On the Relation between Rigging Inner Product and Master Constraint Direct Integral Decomposition
• Invariant Perfect Tensors
• Quasi-Local Energy in Loop Quantum Gravity
• Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions
• Scalar curvature operator for models of loop quantum gravity on a cubical graph
• Topspin Networks in Loop Quantum Gravity
• Spin-foam model for gravity coupled to massless scalar field
• Discrete Gravity on Random Tensor Network and Holographic Rényi Entropy
• Loop quantum gravity and cosmological constant
• Geometric parametrization of $SO(D+1)$ phase space of all dimensional loop quantum gravity
• Superposition type coherent states in all dimensional loop quantum gravity
• Extension of Loop Quantum Gravity to Metric Theories beyond General Relativity
• Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
• Consistency check on the fundamental and alternative flux operators in loop quantum gravity
• Canonical loop quantization of the lowest-order projectable Horava gravity
• Alternative dynamics in loop quantum Brans-Dicke cosmology
• Quantum geometry and effective dynamics of Janis-Newman-Winicour singularities
• One vertex spin-foams with the Dipole Cosmology boundary
• The effective dynamics of weak coupling loop quantum gravity
• The thermodynamics of isolated horizons in loop quantum gravity
• Solar system constraints of a polymer black hole in loop quantum gravity
• Spin foam amplitude of the black-to-white hole transition
• The continuum approach to the BF vacuum: the U(1) case
• Loop quantum modified gravity and its cosmological application
• Experimental Simulation of Loop Quantum Gravity on a Photonic Chip
• Anomaly freedom of the vector modes with holonomy corrections in perturbative Euclidean loop quantum gravity
• SU(2) Flat Connection on Riemann Surface and Twisted Geometry with Cosmological Constant
• Probing loop quantum effects through solar system experiments: observational signatures and parameter constraints
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Quasinormal modes of a charged loop quantum black hole
• Influence of Quantum Correction on Kerr Black Hole in Effective Loop Quantum Gravity via Shadows and EHT Results
• The Hilbert space of Chern-Simons theory on the cylinder. A Loop Quantum Gravity approach
• Fermions in Loop Quantum Gravity and Resolution of Doubling Problem
• Gravitational waves for eccentric extreme mass ratio inspirals of self-dual spacetime
• Connection Dynamics for Higher Dimensional Scalar-Tensor Theories of Gravity
• On the polymer quantization of connection theories: graph coherent states
• Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property
• Dynamics of k-essence in loop quantum cosmology
• Loop quantum cosmology from an alternative Hamiltonian
• Microscopic states of Kerr black holes from boundary-bulk correspondence
• Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory
• Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing
• Hamiltonian structure and connection-dynamics of Weyl gravity
• A Path-integral for the Master Constraint of Loop Quantum Gravity
• Gravitational waves with generalized holonomy corrections
• Energy conditions in new model of loop quantum cosmology
• Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
• Fermion coupling to loop quantum gravity: canonical formulation
• Generalized Interacting Dark Energy Model and Loop Quantum Cosmology
• Graph coherent states for loop quantum gravity
• Reformulation of Boundary BF Theory Approach to Statistical Explanation of the Entropy of Isolated Horizons
• On the gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity
• Graphical method in loop quantum gravity: I. Derivation of the closed formula for the matrix element of the volume operator
• The kernel and the injectivity of the EPRL map
• Loop quantum cosmology in 2+1 dimension
• Circular orbits and accretion disk around a deformed-Schwarzschild black hole in loop quantum gravity
• Loop representation and r-Fock measures for $SU(N)$ gauge theories
• Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term
• The averaged tensors of the relative energy-momentum and angular momentum in general relativity and some their applications
• Relating spin-foam to canonical loop quantum gravity by graphical calculus
• Random Invariant Tensors
• Holographic equipartition from first order action
• Exploring the Tomlin-Varadarajan quantum constraints in $U(1{)}^3$ loop quantum gravity: solutions and the Minkowski theorem
• Spin foam propagator: A new perspective to include a cosmological constant
• Thermodynamics in new model of loop quantum cosmology
• Graphical method in loop quantum gravity: II. The Hamiltonian constraint and inverse volume operators
• Alternative $k=-1$ loop quantum cosmology
• Covariant effective spacetimes of spherically symmetric electrovacuum with a cosmological constant
• Aspects of quantum gravity
• Weak gravitational interaction of fermions: quantum viewpoint
• Fix Immirzi parameter by quasinormal modes in four and higher spacetime dimensions
• The Entropy of Nonrotating Isolated Horizons in Lovelock Theory from Loop Quantum Gravity
• The Entropy of BTZ Black Hole from Loop Quantum Gravity
• Master constraint approach to quantum-reduced loop gravity
• Quantum Oppenheimer-Snyder models in loop quantum cosmology with Lorentz term
• Semi-classical States in Homogeneous Loop Quantum Cosmology
• Conformally Invariant Brans-Dicke Loop Quantum Cosmology: A Quantum Geometric Model of Linking Theory
• Loop Quantum Vector-Tensor Gravity and Its Spherically Symmetric Model
• Homogeneous-isotropic sector of loop quantum gravity: new approach
• Correction to the quantum relation of photons in the Doppler effect based on a special Lorentz violation model
• Emergence of scalar matter from spinfoam model
• Expansion operators in spherically symmetric loop quantum gravity
• Geometrical Quantum Time in the $U(1{)}^3$ Model of Euclidean Quantum Gravity
• Loop quantum cosmological model from ADM Hamiltonian
• Periodic Orbits and Gravitational Wave Radiation of Black Hole in EGB gravity
• Cosmological implications of the hydrodynamical phase of group field theory
• Effective Dynamics of Loop Quantum Kaluza-Klein Cosmology
• Deparametrization and quantization of scalar-tensor gravity and its cosmological model
• Image of a quantum-corrected black hole without Cauchy horizons illuminated by a static thin accretion disk
• Realization of Dirac quantization in loop quantum gravity
• Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization
• A saddle-point finder and its application to the spin foam model
• Inflationary spectra from a near $\Omega$-deformed space-time transition point in Loop Quantum Cosmology
• Commuting Simplicity and Closure Constraints for 4D Spin Foam Models
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
• Loop Quantization of a Model for D=1+2 (Anti)de Sitter Gravity Coupled to Topological Matter
• Properties of the Rovelli-Smolin-DePietri volume operator in the spaces of monochromatic intertwiners
• Local density matrices of many-body states in the constant weight subspaces
• Effective Theories of Quantum Cosmology
• Quaternion-Loop Quantum Gravity
• Counter-term for the Palatini action of general relativity
• Quantum Dyanmics of Loop Quantum Gravity
• Effective dynamics of Janis-Newman-Winicour spacetime
• The Semiclassical limit of $SU(3)$ Gauge Field Coherent States: Peakedness and Overlap Functions
• Higher-dimensional quantum-corrected Oppenheimer-Snyder model with a cosmological constant
• Connection dynamics of a gauge theory of gravity coupled with matter
• Loop quantization of a 3D Abelian BF model with sigma-model matter
• Mechanics of Isolated Horizons in Scalar-Tensor Theories
• 2+1 dimensional loop quantum cosmology of Bianchi I models
• Anomaly-free representations of the holonomy-flux algebra
• Critical collapse of a massive scalar field in semi-classical loop quantum gravity
• Complete loop quantization of a dimension 1+2 Lorentzian gravity theory
• Semiclassical Length Measure from a Quantum-Gravity Wave Function