Dynamics of Loop Quantum Gravity and Spin Foam Models in Three Dimensions

The goal of the spin foam approach 1 is to construct a mathematically well defined notion of path integral for non-perturbative quantum GR as a devise for computing the ‘dynamics’ of the theory. By ‘dynamics’ here we mean the characterization of the kernel of the quantum constraints given by the representation of the classical constraints in connection variables, schematically, Gi = DaE a i , Vb = E a i F i ab, and S = E EFab(A) . Spin foam models have been studied as an attempt to give an explicit construction of the generalized projection operator P from the kinematical Hilbert space Hkin, where the constraints above are defined as operators, into their kernel Hphys. A tentative regularization of the formal projector into the kernel of S(x) and V (x)