Spin foam quantization of SO(4) Plebanski's action

Details Spin foam quantization of SO(4) Plebanski's action Spin foam quantization of SO(4) Plebanski's action

2002-03-15

arxiv.org/abs/gr-qc/0203058v5

Adv.Theor.Math.Phys. 5 (2002) 947-968; Erratum-Adv.Theor.Math.Phys. 6 (2003) 593-595

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Main conclusions in first part changed due to correction in the derivation

Scientific paper

The goal of this work is two-fold. In the first part of this paper we regard classical Plebanski's action as a BF action supplemented by constraints. We introduce a spin foam model for Riemannian general relativity by systematically implementing these constraints as restrictions on paths in the state-sum of the BF theory. The spin foam model obtained is precisely the Barrett-Crane model. This provides a clear-cut connection of the model with a simplicial action. In the second part of the paper we study the quantization of the effective action corresponding to the degenerate sectors of Plebanski's theory and obtain a very simple spin foam model. This model turns out to be precisely the one introduced by De Pietri et al. as an alternative to the one proposed by Barrett and Crane.

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