Quaternion Higgs and the Electroweak Gauge Group

TL;DR

This paper demonstrates that quaternion quantum mechanics naturally leads to the electroweak gauge group, clarifying the role of Higgs fields and their solutions within this framework.

Contribution

It establishes a connection between quaternion invariance and the electroweak gauge group, providing new insights into Higgs scalar solutions in quaternion quantum mechanics.

Findings

Quaternion invariance corresponds to the Glashow group.

Minimal four Higgs fields determine the gauge symmetry.

Complex projection of the Lagrangian reveals physical significance.

Abstract

We show that, in quaternion quantum mechanics with a complex geometry, the minimal four Higgs of the unbroken electroweak theory naturally determine the quaternion invariance group which corresponds to the Glashow group. Consequently, we are able to identify the physical significance of the anomalous Higgs scalar solutions. We introduce and discuss the complex projection of the Lagrangian density.