Constraining the Higgs Mechanism: Ontological Worries and the Prospects for an Algebraic Cure

Abstract

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.