Dynamics of loop quantum gravity and spin foam models in three dimensions

Abstract

We present a rigorous regularization of Rovellis's generalized projection operator in canonical 2+1 gravity. This work establishes a clear-cut connection between loop quantum gravity and the spin foam approach in this simplified setting. The point of view adopted here provides a new perspective to tackle the 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