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http://arxiv.org/abs/1202.5039

Degenerate Plebanski Sector and its Spin Foam Quantization

Authors: Sergei Alexandrov

(Submitted on 22 Feb 2012)

Abstract: We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact provides its spin foam quantization and allows to test various approaches of imposing the simplicity constraints. Our analysis suggests a unique method of imposing the constraints which leads to a consistent and well defined spin foam model.

Alexandrov clarifies the role of the first and second class constraints, especially of the simplicity constraints. He shows that in order to recover the well-known Crane-Yetter model for the degenerate sector one has to impose the constraints classicaly i.e. by inserting delta functions which changes the measure and therefore the vertex aamplitude.

He shows that the method used by EPRL and FK is not sufficient to suppress the quantum fluctuations related to these constraints and that their method does not lead to the (correct) Crane-Yetter model! In addition he shows that the Immirzi parameter drops out in the final theory and that effects regarding its quantization are artificial.

What next? Application of these methods to modify (i.e. to correct) the quantization of the EPRL and FK model. I am convinced that this will result in a new vertex amplitude.

marcus: I nominate this paper as the most important one for your next poll: the picks for first quarter 2012 - most important QG paper

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# Constraints, measure and vertex amplitude in LQG

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