An elementary introduction to loop quantum gravity

Abstract

An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in five lectures, including exercises, and requires only little prior knowledge of quantum mechanics, gauge theory, and general relativity. The main aim of these lectures is to provide non-experts with an elementary understanding of loop quantum gravity and to evaluate the state of the art of the field. Technical details are avoided wherever possible.

48+14 pages, 8 figures

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• Quantum Geometry and Black Hole Entropy
• Black Holes at the LHC
• Quantum Theory of Gravity I: Area Operators
• Isolated and dynamical horizons and their applications
• Absence of Singularity in Loop Quantum Cosmology
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Quantum Spin Dynamics (QSD)
• The Spin Foam Approach to Quantum Gravity
• Black Hole Entropy from Loop Quantum Gravity
• LQG vertex with finite Immirzi parameter
• Spin Foam Models for Quantum Gravity
• Robustness of key features of loop quantum cosmology
• Dust as a Standard of Space and Time in Canonical Quantum Gravity
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• QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
• Projective Techniques and Functional Integration
• Asymptotic safety of gravity and the Higgs boson mass
• ``Sum over Surfaces'' form of Loop Quantum Gravity
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• Colored Tensor Models - a Review
• Representations of the holonomy algebras of gravity and non-Abelian gauge theories
• Lorentz invariance and quantum gravity: an additional fine-tuning problem?
• Black hole evaporation: A paradigm
• Differential Geometry on the Space of Connections via Graphs and Projective Limits
• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
• Matter matters in asymptotically safe quantum gravity
• The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
• Twisted geometries: A geometric parametrisation of SU(2) phase space
• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
• A Quantum Gravity Extension of the Inflationary Scenario
• Loop quantization of the Schwarzschild black hole
• Polyhedra in loop quantum gravity
• The physical hamiltonian in nonperturbative quantum gravity
• Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Time and a physical Hamiltonian for quantum gravity
• Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories
• Cosmology from Group Field Theory Formalism for Quantum Gravity
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Homogeneous cosmologies as group field theory condensates
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
• Counting surface states in the loop quantum gravity
• Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
• On the support of the Ashtekar-Lewandowski measure
• Gravity quantized
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
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• SU(2) Loop Quantum Gravity seen from Covariant Theory
• Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
• Black hole entropy and isolated horizons thermodynamics
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• Quantum oscillations and black hole ringing
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• Large scale effective theory for cosmological bounces
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• Bouncing cosmologies from quantum gravity condensates
• Tensorial methods and renormalization in Group Field Theories
• Decorated tensor network renormalization for lattice gauge theories and spin foam models
• Numerical evidence for a phase transition in 4d spin foam quantum gravity
• Ten questions on Group Field Theory (and their tentative answers)
• Jones Polynomials for Intersecting Knots as Physical States of Quantum Gravity
• Gravitons and Loops
• Evidence for Asymptotic Safety from Lattice Quantum Gravity
• Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
• New Variables for Classical and Quantum Gravity in all Dimensions I. Hamiltonian Analysis
• Anomaly-free perturbations with inverse-volume and holonomy corrections in Loop Quantum Cosmology
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Spin Foams and Canonical Quantization
• Lorentz covariance of loop quantum gravity
• Entanglement Entropy in Loop Quantum Gravity
• Introduction to Loop Quantum Gravity and Spin Foams
• Lattice Quantum Gravity and Asymptotic Safety
• Black Hole Entropy from complex Ashtekar variables
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
• Testing the Master Constraint Programme for Loop Quantum Gravity II. Finite Dimensional Systems
• Lorentzian spinfoam propagator
• Photons from quantized electric flux representations
• New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
• Quantum Gravity via Causal Dynamical Triangulations
• Hydrodynamic Long-Time tails From Anti de Sitter Space
• Stable cosmological models driven by a free quantum scalar field
• Group field theory as the 2nd quantization of Loop Quantum Gravity
• A new perspective on cosmology in Loop Quantum Gravity
• Linking covariant and canonical LQG: new solutions to the Euclidean Scalar Constraint
• Testing the Master Constraint Programme for Loop Quantum Gravity IV. Free Field Theories
• Exact solutions for Big Bounce in loop quantum cosmology
• New scalar constraint operator for loop quantum gravity
• Hamiltonian operator for loop quantum gravity coupled to a scalar field
• Emergence of a low spin phase in group field theory condensates
• Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
• Quantum Reduced Loop Gravity: Semiclassical limit
• Reconstructing AdS/CFT
• Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories
• Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity
• Spacetime thermodynamics without hidden degrees of freedom
• Supersymmetric Spin Networks and Quantum Supergravity
• Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I
• Observational Exclusion of a Consistent Quantum Cosmology Scenario
• Gravitons from a loop representation of linearised gravity
• Generalized quantum gravity condensates for homogeneous geometries and cosmology
• Towards a loop representation for quantum canonical supergravity
• Consistent Probabilities in Wheeler-DeWitt Quantum Cosmology
• Quantum group spin nets: refinement limit and relation to spin foams
• Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
• Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Master Constraint Operator in Loop Quantum Gravity
• Hilbert space structure of covariant loop quantum gravity
• Discreteness corrections and higher spatial derivatives in effective canonical quantum gravity
• Geometric temperature and entropy of quantum isolated horizons
• Semiclassical quantisation of space-times with apparent horizons
• Constraint algebra in LQG reloaded : Toy model of an Abelian gauge theory - II Spatial Diffeomorphisms
• Towards Loop Quantum Gravity without the time gauge
• The Hamiltonian constraint in Polymer Parametrized Field Theory
• A quantum reduction to Bianchi I models in loop quantum gravity
• A symmetric scalar constraint for loop quantum gravity
• Linking covariant and canonical LQG II: Spin foam projector
• Bubble divergences and gauge symmetries in spin foams
• From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
• Duality between Spin networks and the 2D Ising model
• Loop Quantization of Maxwell Theory and Electric Charge Quantization
• Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity: Diffeomorphism Covariance
• Group Averaging and Refined Algebraic Quantization
• Wheeler-DeWitt quantization and singularities
• New Variables for Classical and Quantum Gravity in all Dimensions V. Isolated Horizon Boundary Degrees of Freedom
• Identifying cosmological perturbations in group field theory condensates
• A Lorentz-Covariant Connection for Canonical Gravity
• Symmetry Reduction of Loop Quantum Gravity
• Coherent states, quantum gravity and the Born-Oppenheimer approximation, II: Compact Lie Groups
• General relativity in the radial gauge: Reduced phase space and canonical structure
• Apparent horizons, black hole entropy and loop quantum gravity
• Loop Quantum Cosmology from Loop Quantum Gravity
• Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations
• Improved regularization from Quantum Reduced Loop Gravity
• Invariant Connections in Loop Quantum Gravity
• Squeezed vacua in loop quantum gravity
• A quantum reduction to spherical symmetry in loop quantum gravity
• The Wald entropy formula and loop quantum gravity
• Lorentz violation naturalness revisited
• The consistent histories approach to loop quantum cosmology
• On background-independent renormalization of spin foam models
• A local Hamiltonian for spherically symmetric gravity coupled to a scalar field
• A note on quantum supergravity and AdS/CFT
• Some notes on the Kodama state, maximal symmetry, and the isolated horizon boundary condition
• Hamiltonian constraint in Euclidean LQG revisited: First hints of off-shell Closure

Cited by in corpus (22)

• Reduced Loop Quantization with four Klein-Gordon Scalar Fields as Reference Matter
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Probability of Warm Inflation in Loop Quantum Cosmology
• Statistical equilibrium of tetrahedra from maximum entropy principle
• Thermal quantum gravity condensates in group field theory cosmology
• Constraining the loop quantum gravity parameter space from phenomenology
• Thermal representations in group field theory: squeezed vacua and quantum gravity condensates
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Scalar curvature operator for models of loop quantum gravity on a cubical graph
• Quantum Corrected Polymer Black Hole Thermodynamics: Mass Relations and Logarithmic Entropy Correction
• The Quantum Gravity Disk: Discrete Current Algebra
• Generalized Interacting Dark Energy Model and Loop Quantum Cosmology
• Modified dispersion relations, inflation and scale invariance
• Towards quantum gravity with neural networks: Solving the quantum Hamilton constraint of U(1) BF theory
• Graph coherent states for loop quantum gravity
• Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
• Intertwiner Entanglement Excitation and Holonomy Operator
• The Physical Relevance of the Fiducial Cell in Loop Quantum Cosmology
• Spherically-symmetric geometries in a matter reference frame as quantum gravity condensates
• On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC
• A Loop Quantum Gravity Inspired Action for the Bosonic String and Emergent Dimensions at Large Scales
• Local and Nonlocal Thermal Field Theory