Alejandro Perez 2003 Class. Quantum Grav. 20 R43 doi:10.1088/0264-9381/20/6/202
Spin foam models for quantum gravity
REVIEW ARTICLEAlejandro Perez
Show affiliationsTOPICAL REVIEW
In this topical review, we review the 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 the main 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.
- PACS
- MSC
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81S10 Geometry and quantization, symplectic methods (See also 53D50)
- Subjects
- Dates
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Issue 6 (21 March 2003)
Received 4 September 2002, in final form 10 December 2002
Published 21 February 2003
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Spin foam models for quantum gravity
Alejandro Perez 2003 Class. Quantum Grav. 20 R43
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