Description
It is often emphasized that spin-foam models could realize a projection on the physical Hilbert space of canonical Loop Quantum Gravity in the spirit of a rigging map construction. If this is indeed the case then the constraints have to vanish in the physical scalar product defined through spin-foams. We analyze the one-vertex expansion of a simple Euclidean spin-foam and find that it annihilates the Euclidean Hamiltonian constraint of canonical Loop Quantum Gravity in 4d. However, the states constructed are special and closely related to BF-theory.
