# Higgs fields induced by Yang--Mills type Lagrangians on gauge-natural prolongations of principal bundles

## TL;DR

This paper introduces a new way to define classical Higgs fields in gauge-natural invariant Yang--Mills theories by using canonical conserved quantities, exemplified through the gluon Lagrangian on SU(3) connections.

## Contribution

It proposes a novel definition of Higgs fields based on gauge-natural invariance and conserved quantities, with an explicit example involving gluon fields.

## Key findings

- Defined classical Higgs fields via gauge-natural conserved quantities.
- Applied the framework to the gluon Lagrangian on SU(3) connections.
- Established a canonical Higgs field through reductive structure.

## Abstract

We address some new issues concerning spontaneous symmetry breaking. We define classical Higgs fields for gauge-natural invariant Yang--Mills type Lagrangian field theories through the requirement of the existence of {\em canonical} covariant gauge-natural conserved quantities. As an illustrative example we consider the `gluon Lagrangian', i.e. a Yang--Mills Lagrangian on the $(1,1)$-order gauge-natural bundle of $SU(3)$-principal connections, and canonically define a `gluon' classical Higgs field through the split reductive structure induced by the kernel of the associated gauge-natural Jacobi morphism.