Boundary terms in the Barrett–Crane spin foam model and consistent gluing

We extend the lattice gauge theory-type derivation of the Barrett–Crane spin foam model for quantum gravity to other choices of boundary conditions, resulting in different boundary terms, and re-analyze the gluing of 4-simplices in this context. This provides a consistency check of the previous derivation. Moreover we study and discuss some possible alternatives and variations that can be made to it and the resulting models.