Loop quantum gravity - a short review

Abstract

In this article we review the foundations and the present status of loop quantum gravity. It is short and relatively non-technical, the emphasis is on the ideas, and the flavor of the techniques. In particular, we describe the kinematical quantization and the implementation of the Hamilton constraint, as well as the quantum theory of black hole horizons, semiclassical states, and matter propagation. Spin foam models and loop quantum cosmology are mentioned only in passing, as these will be covered in separate reviews to be published alongside this one.

23 pages, 7 figures, talk delivered at the workshop "Foundations of Space and Time - Reflections on Quantum Gravity" in honor of George Ellis, STIAS, Stellenbosch, South Africa, 10-14 August 2009. v3: bibliography updated, typos removed, some additional comments

References in corpus (25)

• Quantum Nature of the Big Bang
• LQG vertex with finite Immirzi parameter
• The loop-quantum-gravity vertex-amplitude
• Black hole entropy and SU(2) Chern-Simons theory
• Anomaly freedom in perturbative loop quantum gravity
• Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
• Gravity quantized
• Quantum field theory on a cosmological, quantum space-time
• Spectral Analysis of the Volume Operator in Loop Quantum Gravity
• Detailed black hole state counting in loop quantum gravity
• Black hole entropy quantization
• Counting black hole microscopic states in loop quantum gravity
• The combinatorics of the SU(2) black hole entropy in loop quantum gravity
• Physical time and other conceptual issues of QG on the example of LQC
• Flux-area operator and black hole entropy
• A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
• Black Hole Entropy, Loop Gravity, and Polymer Physics
• Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex
• Generic isolated horizons in loop quantum gravity
• Comment on "Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?" by B. Dittrich and T. Thiemann
• Entropy calculation for a toy black hole
• Statistical description of the black hole degeneracy spectrum
• Toward explaining black hole entropy quantization in loop quantum gravity
• Black hole radiation spectrum in LQG: Isolated Horizon framework
• Wave propagation on a random lattice