Massive Yang-Mills fields, translational and nonsemisimple gauge symmetry

TL;DR

This paper demonstrates that localizing nonsemisimple internal symmetries results in massive gauge fields, introduces nonlinear models with translational symmetry, and offers a new interpretation of the Stueckelberg mechanism.

Contribution

It shows that gauge fields associated with translation generators become massive under localization of nonsemisimple symmetries and introduces nonlinear models with local translational symmetry.

Findings

Localization of nonsemisimple symmetries yields massive gauge fields.

Nonlinear models with local translational symmetry are constructed.

A simple interpretation of the Stueckelberg mechanism is proposed.

Abstract

Gauge fields of semisimple groups of internal symmetries are massless and require the special techniques for guarantee their mass. Massive mechanisms usually contain transformations of shifts typical to nonsemisimple groups. We show that under the localization of nonsemisimple internal symmetry the gauge fields corresponding to translation generators are massive. In addition, we introduce nonlinear generalizations of well-known models, with local translational symmetry and as a result, the massive gauge fields. Thus, the local Galilean symmetry is realized on a special pair of scalar fields, leading to massive electrodynamics, and the localization of the Euclidean group leads to massive non-Abelian theory without matter fields. We propose a simple interpretation of the Stueckelberg mechanism.