Loop quantum gravity and quanta of space: a primer

Abstract

We present a straightforward and self-contained introduction to the basics of the loop approach to quantum gravity, and a derivation of what is arguably its key result, namely the spectral analysis of the area operator. We also discuss the arguments supporting the physical prediction following this result: that physical geometrical quantities are quantized in a non-trivial, computable, fashion. These results are not new; we present them here in a simple form that avoids the many non-essential complications of the first derivations.

11 pages

References in corpus (28)

• Discreteness of area and volume in quantum gravity
• Quantum Geometry and Black Hole Entropy
• Quantum Theory of Gravity I: Area Operators
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Spin Networks and Quantum Gravity
• Weaving a classical geometry with quantum threads
• Spin Foam Models
• ``Sum over Surfaces'' form of Loop Quantum Gravity
• Representations of the holonomy algebras of gravity and non-Abelian gauge theories
• Spin Network States in Gauge Theory
• Quantum Spin Dynamics (QSD) II
• The physical hamiltonian in nonperturbative quantum gravity
• Quantum Background Independence In String Theory
• Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity
• The Immirzi parameter in quantum general relativity
• Counting surface states in the loop quantum gravity
• Representation Theory of Analytic Holonomy C* Algebras
• On Quantum Statistical Mechanics of a Schwarzschild Black Hole
• Gravitons and Loops
• Quantum geometry with intrinsic local causality
• Recent Developments in Non-Perturbative Quantum Gravity
• On the relation between the connection and the loop representation of quantum gravity
• OUTLINE OF A GENERALLY COVARIANT QUANTUM FIELD THEORY AND A QUANTUM THEORY OF GRAVITY
• Finite, diffeomorphism invariant observables in quantum gravity
• Extended Loops: A New Arena for Nonperturbative Quantum Gravity
• Nonperturbative dynamics for abstract (p,q) string networks
• Vassiliev invariants: a new framework for quantum gravity
• The Gauss Linking Number in Quantum Gravity

Cited by in corpus (27)

• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
• The projector on physical states in loop quantum gravity
• Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
• From lattice BF gauge theory to area-angle Regge calculus
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Hypersurface foliation approach to renormalization of ADM formulation of gravity
• A discrete history of the Lorentzian path integral
• Early Universe Dynamics in Semi-Classical Loop Quantum Cosmology
• Inverse volume corrections to emergent tachyonic inflation in loop quantum cosmology
• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• A Noncommutative Deformation of General Relativity
• Reliability of the local truncations for the random tensor models renormalization group flow
• Sommerfeld's quantum condition of action and the spectra of Schwarzschild black hole
• Flowing in discrete gravity models and Ward identities: A review
• On the counting of black hole states in loop quantum gravity
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• Asymptotic black hole quasinormal frequencies
• An analytical computation of asymptotic Schwarzschild quasinormal frequencies
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Compact anisotropic stars with membrane - a new class of exact solutions to the Einstein field equations
• Infinite Degeneracy of States in Quantum Gravity
• Emergence of General Relativity from Loop Quantum Gravity: A Summary
• Searching for electrovac solutions to Einstein--Maxwell equations with the help of computer algebra system GRG-EC
• White dwarfs and generalized uncertainty principle
• Length versus time-interval discreteness in 2+1 Lorentzian canonical quantum gravity