In this topical review, we reviewthe present status of the spin foam formulation of nonperturbative (backgroundindependent) quantum gravity. The topical review is divided into two parts. In the first part, we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Riemannian threedimensional gravity is used as a simple example to illustrate conceptual issues and themain goals of the approach. The main features of the various existing models for fourdimensional gravity arealso presented here. We conclude with a discussion of important questions tobe addressed in four dimensions (gauge invariance, discretization independence, etc).In the second part, we concentrate on the definition of the Barrettâ€“Cranemodel. 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 Barrettâ€“Crane model in this framework and review the finiteness results obtained for both its Riemannian and its Lorentzian variants.

Authors: Perez A.  Pages: 62 Year: 2003 
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