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It is often emphasized that spin-foam models could realize a projection onthe physical Hilbert space of canonical Loop Quantum Gravity (LQG). As a firsttest we analyze the one-vertex expansion of a simple Euclidean spin-foam. Wefind that for fixed Barbero-Immirzi parameter \gamma=1 the one vertex-amplitudein the KKL prescription annihilates the Euclidean Hamiltonian constraint ofLQG. Since for \gamma=1 the Lorentzian part of the Hamiltonian constraint doesnot contribute this gives rise to new solutions of the Euclidean theory.Furthermore, we find that the new states only depend on the diagonal matrixelements of the volume. This seems to be a generic property when applying thespin-foam projector.

Linking covariant and canonical LQG: new solutions to the Euclidean Scalar Constraint