Dirac Fields on Spacelike Hypersurfaces, Their Rest-Frame Description and Dirac Observables

摘要

Grassmann-valued Dirac fields together with the electromagnetic field (thepseudoclassical basis of QED) are reformulated on spacelike hypersurfaces inMinkowski spacetime and then restricted to Wigner hyperplanes to get theirdescription in the rest-frame Wigner-covariant instant form of dynamics. Thecanonical reduction to the Wigner-covariant Coulomb gauge is done in the restframe. It is shown, on the basis of a geometric incosistency, that thedescription of fermions is incomplete, because there is no bosonic carrier ofthe spin structure describing the trajectory of the electric current inMinkowski spacetime, as it was already emphasized in connection with the firstquantization of spinning particles in a previous paper.