DIRAC FIELDS ON SPACELIKE HYPERSURFACES, THEIR REST-FRAME DESCRIPTION AND DIRAC OBSERVABLES

Abstract

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