Unification of SU(2)xU(1) Using a Generalized Covariant Derivative and U(3)

TL;DR

This paper proposes a generalized covariant derivative to unify the electroweak model with an extended gauge group, addressing hypercharge assignment issues and revealing a new scalar boson that decouples from other particles.

Contribution

It introduces a novel generalized covariant derivative involving vector and scalar fields, unifying SU(2) and U(1) within a U(3) framework, and resolves hypercharge assignment problems.

Findings

Successful unification of electroweak interactions using the generalized derivative.

Correct hypercharge assignments achieved with a special U(3) representation.

Emergence of a decoupled scalar boson in the model.

Abstract

A generalization of the Yang-Mills covariant derivative, that uses both vector and scalar fields and transforms as a 4-vector contracted with Dirac matrices, is used to simplify and unify the Glashow-Weinberg-Salam model. Since SU(3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U(3) to obtain all the correct quantum numbers. A surplus gauge scalar boson emerges in the process, but it uncouples from all other particles.