Spin Foam Models for Quantum Gravity

Abstract

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.

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

References in corpus (8)

• Background Independent Quantum Gravity: A Status Report
• Diffeomorphisms and spin foam models
• SU(2) Loop Quantum Gravity seen from Covariant Theory
• Asymptotics of Relativistic Spin Networks
• Asymptotics of 6j and 10j symbols
• Non-perturbative summation over 3D discrete topologies
• Cosmological Deformation of Lorentzian Spin Foam Models
• On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables

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