Real Spinor Fields and the Electroweak Interaction

The space of real spinor fields of a given massm>0 in Minkowski space is the direct sum of two irreducibly invariant subspaces under the connected Poincaré groupP. These subspaces admit uniqueP-invariant positive-energy complex unitarizable structures, in terms of which they are unitarily and canonically equivalent to the conventional “left electron” and “right positron” subspaces defined by the Dirac equation. Space reversalPand time reversalTactP-covariantly as antiunitary operators on the real fields. They also extend to the complex fields, in terms of whichPexchanges the two subspaces, whileTacts separately on each. Whenm=0, the identical formalism produces a (rigorous) version of the conventional neutrino formalism. The restriction to the real context of the conventional spinor-vector interaction is equivalent to the conventionalV−Ainteraction together with a computationally equivalent form of quantum electrodynamics in which the right electron and left electron are redundant.