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. (shrink)

Two alternative accounts of quantum spontaneous symmetry breaking (SSB) are compared and one of them, the decompositional account in the algebraic approach, is argued to be superior for understanding quantum SSB. Two exactly solvable models are given as applications of our account -- the Weiss-Heisenberg model for ferromagnetism and the BCS model for superconductivity. Finally, the decompositional account is shown to be more conducive to the causal explanation of quantum SSB.

I discuss Earman's program to achieve an objective account of the Higgs mechanism within the C∗ algebraic approach to quantum field theory. Pointing to three results obtained within this approach, I argue that if one follows Earman and understands the Higgs mechanism as a constraint, it appears to be a genuine quantum phenomenon that does not simply arise through the correspondence principle. This casts further this casts doubts on the validity of the Dirac conjecture that identifies first-class constraints and gauge (...) transformations and that provides a major motivation for both Earman's program and Struyve's demonstration that a gauge-invariant account of the Higgs mechanism can be accomplished at the classical level. (shrink)