A geometry for the electroweak field

TL;DR

This paper proposes a geometric framework for the electroweak field using a nonlinear map from spinor space to a tangent bundle, offering a novel perspective that may facilitate bosonization in four-dimensional spacetime.

Contribution

It introduces a new geometric approach to the electroweak theory via a nonlinear map from spinors to tetrads, suggesting a potential path for bosonization.

Findings

Electroweak field modeled through a geometric nonlinear map.

The approach favors the bosonic nature of the electroweak field.

Potential implications for quantization and bosonization in 4D.

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.