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We study a generalized action for gravity as a constrained BF theory, and itsrelationship with the Plebanski action. We analyse the discretization of theconstraints and the spin foam quantization of the theory, showing that it leadsnaturally to the Barrett-Crane spin foam model for quantum gravity. Ouranalysis holds true in both the Euclidean and Lorentzian formulation.Comment: 15 pages, revtex; a sign corrected (area spectrum); some of these  results were presented in a preliminary form in gr-qc/0103081; v2: improved  presentation of the results, some changes in the text; to appear in Phys.  Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Barrett-Crane spin foam model from generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>BF</mml:mi></mml:math>-type action for gravity

Barrett-Crane spin foam model from generalizedBF-type action for gravity