Spin Foam Models for Quantum Gravity

Details Spin Foam Models for Quantum Gravity Spin Foam Models for Quantum Gravity

2003-01-27

arxiv.org/abs/gr-qc/0301113v2

Class.Quant.Grav. 20 (2003) R43

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Topical review, to appear in CQG. Typos corrected and new references added

Scientific paper

In this article we review the present status of the spin foam formulation of non-perturbative (background independent) quantum gravity. The article is divided in two parts. In the first part we present a general introduction to the main ideas emphasizing their motivations from various perspectives. Riemannian 3-dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for 4-dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc.). In the second part we concentrate on the definition of the Barrett-Crane model. We present the main results obtained in this framework from a critical perspective. Finally we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett-Crane model in this framework and review the finiteness results obtained for both its Riemannian as well as its Lorentzian variants.

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