  We describe a class of spin foam models of four-dimensional quantum gravity
which is based on the integration of the tetrad one-forms in the path integral
for the Palatini action of General Relativity. In the Euclidian gravity case
this class of models can be understood as a modification of the Barrett-Crane
spin foam model. Fermionic matter can be coupled by using the path integral
with sources for the tetrads and the spin connection, and the corresponding
state sum is based on a spin foam where both the edges and the faces are
colored independently with the irreducible representations of the spacetime
rotations group.
