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In the search for a covariant formulation for Loop Quantum Gravity, spinfoams have arised as the corresponding discrete space-time structure and, amongthe different models, the Barrett-Crane model seems the most promising. Here,we study its boundary states and introduce cylindrical functions on both theLorentz connection and the time normal to the studied hypersurface. We callthem projected cylindrical functions and we explain how they would naturallyarise in a covariant formulation of Loop Quantum Gravity.Comment: Latex, 15 page

Projected spin networks for Lorentz connection: linking spin foams and loop gravity