Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity

Details Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity

2001-06-28

arxiv.org/abs/gr-qc/0106091v3

Rept.Prog.Phys.64:1703-1756,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

68 pages, 16 figures, LaTex; v2: minor changes; v3: several points clarified, references added; to appear in Rep. Prog. Phys

Scientific paper

10.1088/0034-4885/64/12/203

This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path integral quantum gravity, lattice field theory, matrix models, category theory, statistical mechanics. We describe the general formalism and ideas of spin foam models, the picture of quantum geometry emerging from them, and give a review of the results obtained so far, in both the Euclidean and Lorentzian case. We focus in particular on the Barrett-Crane model for 4-dimensional quantum gravity.

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