Spin foam quantization of SO(4) Plebański's action
type: Item
instance of: scholarly article
title: Spin foam quantization of SO(4) Plebański's action
zbMATH Open document ID: 1012.83006
author: D. Kharzeev
published in: Advances in Theoretical and Mathematical Physics
publication date: 2002-10-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/gr-qc/0203058
review text: In the present paper Plebanski's action is considered as a BF action supplemented by constraints. The author introduces a spin foam model for Riemannian general relativity by implementing these constraints as restrictions on paths in the state-sum of the BF theory. It is shown that the model obtained is related to the Barrett-Crane model. The author proves that all tetrahedra in the allowed configurations have zero volume. In the second part of the paper the author studies the quantization of the effective action corresponding to the degenerate sectors of Plebanski's theory and ends up with a spin foam model that is precisely the same as introduced by De Pietri et al. It is shown that the four-simplex configurations of the model corresponding to the full Plebanski's action turn out to be entirely contained in the set of configurations of the model of the degenerate sector.
reviewed by: Jürgen Tolksdorf
Mathematics Subject Classification ID: 83C45
Mathematics Subject Classification ID: 83C27
zbMATH DE Number: 1818601
zbMATH Keywords: spin foam model
zbMATH Keywords: Riemannian general relativity
zbMATH Keywords: constraints
zbMATH Keywords: four-simplex configuration
MaRDI profile type: Publication
arXiv ID: gr-qc/0203058
DOI: 10.4310/ATMP.2001.V5.N5.A4
description: scientific article