Classical Higgs fields on gauge gluon bundles

Marcella Palese,Ekkehart Winterroth,G.E Bruno,D.M Creanza,F De Fazio,C Corianò,P Colangelo,S Spagnolo,G Chiodini,E Nappi

doi:10.1051/epjconf/201612900016

Marcella Palese, Ekkehart Winterroth + Show 8 more

Open Access

https://doi.org/10.1051/epjconf/201612900016

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Abstract

Classical Higgs fields and related canonical conserved quantities are defined by invariant variational problems on suitably defined gauge gluon bundles. We consider Lagrangian field theories which are assumed to be invariant with respect to the action of a gauge-natural group. As an illustrative example we exploit the ‘gluon Lagrangian’, i.e. a Yang-Mills Lagrangian on the (1, 1)-order gauge-natural bundle of SU (3)-principal connections. The kernel of the gauge-natural Jacobi morphism for such a Lagrangian, by inducing a reductive split structure, canonically defines a ‘gluon classical Higgs field’.

Highlights

In this note we shall deal with the definition of a classical Higgs field canonically induced by the invariance of a gluon Yang-Mills Lagrangian with respect to the gauge-natural infinitesimal tranformations of the bundle of S U(3)-connections, seen as a (1, 1)-order gauge-natural affine bundle.In particular, the Jacobi equations associated with the gluon Lagrangian define a canonical classical Higgs field, that is a reduction of the relevant principal bundle structure
Classical Higgs fields and related canonical conserved quantities are defined by invariant variational problems on suitably defined gauge gluon bundles
The Jacobi equations associated with the gluon Lagrangian define a canonical classical Higgs field, that is a reduction of the relevant principal bundle structure

Summary

Introduction

In this note we shall deal with the definition of a classical Higgs field canonically induced by the invariance of a gluon Yang-Mills Lagrangian with respect to the gauge-natural infinitesimal tranformations of the bundle of S U(3)-connections, seen as a (1, 1)-order gauge-natural affine bundle.In particular, the Jacobi equations associated with the gluon Lagrangian define a canonical classical Higgs field, that is a reduction of the relevant principal bundle structure. Classical Higgs fields and related canonical conserved quantities are defined by invariant variational problems on suitably defined gauge gluon bundles. We consider Lagrangian field theories which are assumed to be invariant with respect to the action of a gauge-natural group.

Results

Conclusion