so(4) Plebanski Action and Relativistic Spin Foam Model

Details so(4) Plebanski Action and Relativistic Spin Foam Model so(4) Plebanski Action and Relativistic Spin Foam Model

1998-04-26

arxiv.org/abs/gr-qc/9804071v2

Class.Quant.Grav.16:2187-2196,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, REVTeX using AMS fonts. Some minor corrections and improvements

Scientific paper

10.1088/0264-9381/16/7/303

In this note we study the correspondence between the ``relativistic spin foam'' model introduced by Barrett, Crane and Baez and the so(4) Plebanski action. We argue that the $so(4)$ Plebanski model is the continuum analog of the relativistic spin foam model. We prove that the Plebanski action possess four phases, one of which is gravity and outline the discrepancy between this model and the model of Euclidean gravity. We also show that the Plebanski model possess another natural dicretisation and can be associate with another, new, spin foam model that appear to be the $so(4)$ counterpart of the spin foam model describing the self dual formulation of gravity.

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