COMMENTS ABOUT HIGGS FIELDS, NONCOMMUTATIVE GEOMETRY AND THE STANDARD MODEL

TL;DR

This paper reviews the formalism connecting Higgs and Yang-Mills fields through generalized connections, explores variants and their links to noncommutative geometry, and discusses phenomenological implications and algebraic structures.

Contribution

It provides a comprehensive overview of generalized connection formalism, its variants, and their relations to noncommutative geometry and Lie super-algebras.

Findings

Connections between Higgs and Yang-Mills fields via generalized formalism

Discussion of variants and their physical relevance

Analysis of links to noncommutative geometry and algebraic structures

Abstract

We make a short review of the formalism that describes Higgs and Yang Mills fields as two particular cases of an appropriate generalization of the notion of connection. We also comment about the several variants of this formalism, their interest, the relations with noncommutative geometry, the existence (or lack of existence) of phenomenological predictions, the relation with Lie super-algebras etc.