Real spinor fields

Abstract

The Dirac equation is expressed entirely in terms of geometrical quantities by providing a geometrical interpretation for the (-1)1/2 which appears explicitly in the Dirac equation. In the modification of the Dirac electron theory which ensues, the (-1)1/2 appears as the generator of rotations in the spacelike plane orthogonal to the plane containing the electron current and spin vectors. This amounts to a further "relativistic" constraint on the spinor theory and so may be expected to have physical consequences. It does not, however, conflict with well-substantiated features of the Dirac theory.