A $SU(2)$ Generalized Gauge Field Model With Higgs Mechanism

TL;DR

This paper constructs an $SU(2)$ gauge field model using non-commutative geometry that naturally incorporates the Higgs field and demonstrates quantum stability, offering a novel approach to gauge theories.

Contribution

It introduces an $SU(2)$ generalized gauge model with built-in Higgs fields and quantum stability, expanding the framework of gauge theories via non-commutative geometry.

Findings

Includes Higgs field automatically with gauge potentials

Maintains $SU(2) imes ext{pi}_4(SU(2))$ gauge invariance

Proves quantum stability of the model

Abstract

By means of the non-commutative differential geometry, we construct an $SU(2)$ generalized gauge field model. It is of $SU(2) \times \pi_4(SU(2))$ gauge invariance. We show that this model not only includes the Higgs field automatically on the equal footing with ordinary Yang-Mills gauge potentials but also is stable against quantum correlation.