Projected spin network states are the canonical basis of quantum states of
geometry for the most recent EPR-FK spinfoam models for quantum gravity. They
are functionals of both the Lorentz connection and the time normal field. We
analyze in details the map from these projected spin networks to the standard
SU(2) spin networks of loop quantum gravity. We show that this map is not
one-to-one and that the corresponding ambiguity is parameterized by the Immirzi
parameter. We conclude with a comparison of the scalar products between
projected spin networks and SU(2) spin network states.Comment: 14 page