A geometry for the electroweak field

Abstract

The structure of the electroweak theory is suggested by classical geometrical ideas. A nonlinear map is constructed, from a 12-dimensional linear space of three Weyl spinors onto the 12-dimensional tangent bundle of the Stiefel manifold of orthonormal tetrads associated with the Lorentz group -- except, inevitably, for a set of measure zero. In the approach of this paper, the electroweak field is more natural than the Dirac field. This may be just a curiosity since it may not survive quantization, but it suggests a path to bosonization of the electroweak field in (3+1) dimensions.