  The paper investigates the spontaneous breaking of gauge symmetries in gauge
theories from a philosophical angle, taking into account the fact that the
notion of a spontaneously broken local gauge symmetry, though widely employed
in textbook expositions of the Higgs mechanism, is not supported by our leading
theoretical frameworks of gauge quantum theories. In the context of lattice
gauge theory, the statement that local gauge symmetry cannot be spontaneously
broken can even be made rigorous in the form of Elitzur's theorem.
Nevertheless, gauge symmetry breaking does occur in gauge quantum field
theories 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.
