  In this article we lay foundations for a formal relationship of spin foam
models of gravity and BF theory to their continuum canonical formulations.
First the derivation of the spin foam model of the BF theory from the discrete
BF theory action in n dimensions is reviewed briefly. By foliating the
underlying n dimensional simplicial manifold using n-1 dimensional simplicial
hypersurfaces, the spin foam model is reformulated. Then it is shown that spin
network functionals arise naturally on the foliations. The graphs of these spin
network functionals are dual to the triangulations of the foliating
hypersurfaces. Quantum Transition amplitudes are defined. I calculate the
transition amplitudes related to 2D BF theory explicitly and show that these
amplitudes are triangulation independent. The application to the spin foam
models of gravity is discussed briefly.
