Alejandro Perez
Spin Foam Models for Quantum Gravity
Preprint series: ESI preprints

MSC:

83C45 Quantization of the gravitational field

PACS: 04.60.Pp
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
motivation from various perspectives. Riemannian 3-dimensional
gravity is used as a simple example to illustrate conceptual issues and 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.