  The asymptotics of some spin foam amplitudes for a quantum 4-simplex is known
to display rapid oscillations whose frequency is the Regge action. In this
note, we reformulate this result through a difference equation, asymptotically
satisfied by these models, and whose semi-classical solutions are precisely the
sine and the cosine of the Regge action. This equation is then interpreted as
coming from the canonical quantization of a simple constraint in Regge
calculus. This suggests to lift and generalize this constraint to the phase
space of loop quantum gravity parametrized by twisted geometries. The result is
a reformulation of the flat model for topological BF theory from the
Hamiltonian perspective. The Wheeler-de-Witt equation in the spin network basis
gives difference equations which are exactly recursion relations on the
15j-symbol. Moreover, the semi-classical limit is investigated using coherent
states, and produces the expected results. It mimics the classical constraint
with quantized areas, and for Regge geometries it reduces to the semi-classical
equation which has been introduced in the beginning.
