Gauge invariant accounts of the Higgs mechanism

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.

24 pages, no figures, LaTex

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• Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions
• Dressing vs. Fixing: On How to Extract and Interpret Gauge-Invariant Content
• Gauge Invariant Description of the $SU(2)$ Higgs model: Ward identities and Renormalization
• On the Meaning of Local Symmetries: Epistemic-Ontological Dialectics
• The Fröhlich-Morchio-Strocchi mechanism: A underestimated legacy