Loop Quantum Gravity
Abstract
The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a welldeveloped approach to this problem. It is a mathematically welldefined backgroundindependent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planckscale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planckscale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the BekensteinHawking blackhole entropy. (v) Lowenergy calculations, yielding npoint functions well defined in a backgroundindependent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing backgroundindependent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.
 Publication:

Living Reviews in Relativity
 Pub Date:
 July 2008
 DOI:
 10.12942/lrr20085
 Bibcode:
 2008LRR....11....5R
 Keywords:

 Quantum gravity;
 Loop quantum gravity;
 Black Hole;
 Quantum Gravity;
 Loop Quantum Gravity;
 Quantum Cosmology;
 Hamiltonian Constraint