Real Spinor Fields and the Electroweak Interaction

✍ Scribed by Irving Segal

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 241 KB
• Volume: 154
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1997.3213

✦ Synopsis

The space of real spinor fields of a given mass m>0 in Minkowski space is the direct sum of two irreducibly invariant subspaces under the connected Poincare group P. These subspaces admit unique 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 equation.

Space reversal P and time reversal T act P-covariantly as antiunitary operators on the real fields. They also extend to the complex fields, in terms of which P exchanges the two subspaces, while T acts separately on each. When m=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 conventional V&A interaction together with a computationally equivalent form of quantum electrodynamics in which the right electron and left electron are redundant.