Spin foam models for quantum gravity

✍ Scribed by Abhay Ashtekar, Ranjeet S. Tate

• Book ID: 127397709
• Year: 2003
• Tongue: English
• Weight: 747 KB
• Series: CQG 20 R43
• Category: Library
• ISBN: 9810205732

✦ Synopsis

In this topical review, we reviewthe present status of the spin foam formulation of non-perturbative (background-independent) 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 three-dimensional 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 four-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 and its Lorentzian variants.