A Note on the Gauge Group of the Electroweak Interactions

TL;DR

This paper introduces a three-fold covering of the U(2) gauge group to better describe fields with various electric charges in electroweak interactions, laying groundwork for a novel model.

Contribution

It constructs a three-fold covering of U(n) groups and explores representations for modeling electroweak interactions with fractional charges.

Findings

Proposes a three-fold covering of U(2) for electroweak gauge symmetry

Develops a general scheme for U(n) coverings and representations

Lays foundation for a new electroweak interaction model

Abstract

We propose a three-fold covering of the group ${U}(2)$ as a gauge group for the electroweak interactions for the purpose of describing fields with integer and fractional electric charges with respect to the residual electromagnetic gauge group after a spontaneous breaking of the gauge symmetry. In a more general scheme we construct a three-fold covering of ${U} (n)$ and consider for the case $n=2$ several representations which are used in the construction of a model of the electroweak interactions in a subsequent paper.