Gauge symmetry breaking in gauge theories—in search of clarification

Abstract

The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle. Local gauge symmetry itself cannot break spontaneously in quantized gauge theories according to Elitzur's theorem---even though the notion of a spontaneously broken local gauge symmetry is widely employed in textbook expositions of the Higgs mechanism, the standard account of mass generation for the weak gauge bosons in the standard model. Nevertheless, gauge symmetry can be broken in gauge theories, namely, in the form of the breaking of remnant subgroups of the original local gauge group under which the theories typically remain invariant after gauge fixing. The paper discusses the relation between these instances of symmetry breaking and phase transitions and draws some more general conclusions for the philosophical interpretation of gauge symmetries and their breaking.