Real spinor fields and the electroweak interaction
Starting from fact that the space of real spinor fields of mass \(m>0\) on a Minkowskian spacetime is the direct sum of two irreducibly invariant subspaces under the connected Poincaré group \({\mathbf P}\), the author shows that these subspaces admit unique \({\mathbf P}\)-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 electron. It is shown that space reversal \(P\) and time reversal \(T\) act \({\mathbf P}\)-covariantly as anti-unitary operators on these real fields and extend to complex fields in terms of which \(P\) exchanges the two subspaces while \(T\) acts separately on each subspace. When \(m=0\), the identical formalism produces a rigorous version of the usual neutrino formalism. Finally, it is shown that the real context of the usual spinor-vector interaction is equivalent to the V-A interaction, together with a computationally equivalent form of quantum electrodynamics in which the notions of a ``right'' and ``left'' electron are redundant. Contents include: an introduction; complex structures in real spinor fields; discrete symmetries; eigenstates of the basic quantum numbers; interactions in the real spinor formalism; and a discussion.
scientific article; zbMATH DE number 1216772