Path integral representation of spin foam models of 4d gravity

Details Path integral representation of spin foam models of 4d gravity Path integral representation of spin foam models of 4d gravity

2008-06-28

arxiv.org/abs/0806.4640v1

Class.Quant.Grav.25:245010,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages, 6 figures

Scientific paper

10.1088/0264-9381/25/24/245010

We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= gamma < 1, the states can be restricted to SU(2) spin networks.

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