Gauge invariant accounts of the Higgs mechanism

TL;DR

This paper discusses gauge invariant approaches to the Higgs mechanism, arguing that spontaneous symmetry breaking is not essential, and explores different notions of gauge in the Abelian Higgs model within classical field theory.

Contribution

It provides a comprehensive analysis of gauge invariant formulations of the Higgs mechanism, clarifying conceptual issues related to gauge symmetry and spontaneous symmetry breaking.

Findings

Gauge invariant variables can explain the Higgs mechanism without symmetry breaking.

Distinction between two notions of gauge: local transformations and determinism failure.

Classical field theory treatment of the Abelian Higgs model with gauge invariance.

Abstract

The Higgs mechanism gives mass to Yang-Mills gauge bosons. According to the conventional wisdom, this happens through the spontaneous breaking of gauge symmetry. Yet, gauge symmetries merely reflect a redundancy in the state description and therefore the spontaneous breaking can not be an essential ingredient. Indeed, as already shown by Higgs and Kibble, the mechanism can be explained in terms of gauge invariant variables, without invoking spontaneous symmetry breaking. In this paper, we present a general discussion of such gauge invariant treatments for the case of the Abelian Higgs model, in the context of classical field theory. We thereby distinguish between two different notions of gauge: one that takes all local transformations to be gauge and one that relates gauge to a failure of determinism.