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Physics Reports 506, 3-4 (2011) 41-86
Critical Overview of Loops and Foams
Sergey Alexandrov1, Philippe ROCHE1
(2011-05-17)

This is a review of the present status of loop and spin foam approaches to quantization of four-dimensional general relativity. It aims at raising various issues which seem to challenge some of the methods and the results often taken as granted in these domains. A particular emphasis is given to the issue of diffeomorphism and local Lorentz symmetries at the quantum level and to the discussion of new spin foam models. We also describe modifications of these two approaches which may overcome their problems and speculate on other promising research directions.
1:  LPTA - Laboratoire de Physique Théorique et Astroparticules
Physics/General Relativity and Quantum Cosmology
Fulltext link: 
http://fr.arXiv.org/abs/1009.4475