Theory of Classical Higgs Fields. I. Matter Fields

TL;DR

This paper develops a theoretical framework for classical Higgs fields and matter fields within gauge theory, focusing on their geometric representation and symmetry properties in principal bundles.

Contribution

It introduces a geometric description of matter fields with exact symmetry groups using composite bundles associated to principal bundles, emphasizing gauge group actions.

Findings

Matter fields are represented by sections of composite bundles.

Higgs fields are sections of quotient bundles in gauge theory.

The framework clarifies the role of gauge groups in matter field symmetry.

Abstract

Higgs fields are attributes of classical gauge theory on a principal bundle $P\to X$ whose structure Lie group $G$ if is reducible to a closed subgroup $H$. They are represented by sections of the quotient bundle $P/H\to X$. A problem lies in description of matter fields with an exact symmetry group $H$. They are represented by sections of a composite bundle which is associated to an $H$-principal bundle $P\to P/H$. It is essential that they admit an action of a gauge group $G$.