  Spin foam models for gravity or BF theory can be constructed by path integral
formulation of the classical discrete models formulated on simplicial
manifolds. Using this, we discuss the rigorous construction of Lorentzian spin
foam models for gravity and BF theory based on the Gelfand-Naimark theory of
the representations of SL(2,C). First we construct the simplex amplitude for
the BF SL(2,C) model. Next we discuss the implementation of the Barrett-Crane
constraints on this model to derive the spin foam model for gravity. The
non-trivial constraints are the cross simplicity constraints which state that
the sum of the bivectors associated to any two triangles of a quantum
tetrahedron is simple. We do not complete the construction of the model, but
ultimately we derive an equation corresponding to the cross simplicity
constraints that the Lorentzian spin foam model of gravity has to satisfy. In
the appendix we give a simple derivation of the Clebsch-Gordan coefficients for
SL(2,C).
