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We present a rigorous regularization of Rovellis's generalized projectionoperator in canonical 2+1 gravity. This work establishes a clear-cut connectionbetween loop quantum gravity and the spin foam approach in this simplifiedsetting. The point of view adopted here provides a new perspective to tacklethe problem of dynamics in the physically relevant  3+1 case.Comment: To appear in the procedings of the Third International Symposium on  Quantum Theory and Symmetries (QTS3), September 200

DYNAMICS OF LOOP QUANTUM GRAVITY AND SPIN FOAM MODELS IN THREE DIMENSIONS