Dirac fields on spacelike hypersurfaces, their rest-frame description and dirac observables

Grassmann-valued Dirac fields together with the electromagnetic field (the pseudoclassical basis of QED) are reformulated on spacelike hypersurfaces i n Minkowski spacetime and then restricted to Wigner hyperplanes to get thei r description in the rest-frame Wigner-covariant instant form of dynamics. The canonical reduction to the Wigner-covariant Coulomb gauge is done in th e rest frame. It is shown, on the basis of a geometric inconsistency, that the description of fermions is incomplete, because there is no bosonic carr ier of the spin structure describing the trajectory of the electric current in Minkowski space-time, as it was already emphasized in connection with t he first quantization of spinning particles in a previous paper.