Spin foam models for quantum gravity. (English) Zbl 1030.83002

Perez, Alejandro

Classical Quantum Gravity 20, No. 6, R43-R104 (2003).

Summary: In this 62-page topical review the present status of spin foam model construction of non-perturbative (background-independent) quantum gravity is extensively covered.
The first part comprises a general introduction to the chief ideas, clearly emphasizing the motivations from several angles. To illustrate the main concepts the Riemannian three-dimensional gravity is used. Various existing models for four-dimensional gravity with a discussion on related issues like gauge invariance and discretization-dependence are dealt with.
In the second part of the work the Barrett-Crane model is defined and discussed. A combinatorial formulation of spin foam models based on the dual group field theory techniques is also given.

Reviewer: Paninjukunnath Achuthan (Madras)

MSC:

83-02	Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C45	Quantization of the gravitational field

Keywords:

quantum gravity; discretization; Riemannian three-dimensional gravity; gauge invariance; Barrett Crane model