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

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.

20 pages, some oversights corrected

References in corpus (3)

• Topological obstructions in Lagrangian field theories, with an application to 3D Chern-Simons gauge theory
• Lagrangian reductive structures on gauge-natural bundles
• A variational perspective on classical Higgs fields in gauge-natural theories

Cited by in corpus (2)

• Symmetry transformations of extremals and higher conserved quantities: invariant Yang--Mills connections
• The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang-Mills theory on a Minkowskian background