Parallel Transport in Gauge Theory on $M_4 \times Z_2$ Geometry

TL;DR

This paper explores the geometric interpretation of gauge theory on a specific discrete-continuous space, applying it to the electroweak model and analyzing the role of the Higgs field as a gauge component.

Contribution

It extends gauge theory on $M_4 imes Z_2$ to the Weinberg-Salam model, clarifies the geometric meaning of curvatures, and discusses BRST gauge fixing within this framework.

Findings

Geometric interpretation of curvatures in $M_4 imes Z_2$ gauge theory.

Higgs field as a gauge field along the $Z_2$ direction.

Implementation of BRST invariant gauge fixing.

Abstract

We apply the gauge theory on $M_4\times Z_2$ geometry previously proposed by Konisi and Saito to the Weinberg-Salam model for electroweak interactions, especially in order to clarify the geometrical meaning of curvatures in this geometry. Considering the Higgs field to be a gauge field along $Z_2$ direction, we also discuss the BRST invariant gauge fixing in this theory.