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Spin foam models for quantum gravity
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DOI：10.1088/0264-9381/20/6/202.png)
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Abstract
En 中文
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.
Keywords:
STATE-SUM INVARIANTS
FIELD-THEORY
HAMILTONIAN CONSTRAINT
GENERAL-RELATIVITY
DYNAMICS QSD
LORENTZIAN
CONNECTION
SPACE
FORMULATION
VARIABLES
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