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

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

1998-07-08

arxiv.org/abs/hep-th/9807054v1

Int.J.Mod.Phys. A14 (1999) 1877-1910

Physics

High Energy Physics

High Energy Physics - Theory

44 pages, revtex

Scientific paper

10.1142/S0217751X99000956

Grassmann-valued Dirac fields together with the electromagnetic field (the pseudoclassical basis of QED) are reformulated on spacelike hypersurfaces in Minkowski spacetime 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 incosistency, 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 spacetime, as it was already emphasized in connection with the first quantization of spinning particles in a previous paper.

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