Gauge symmetries of Yang-Mills fields

Abstract

We discuss the concept of gauge symmetries of solutions to the Yang-Mills-Higgs field equations and study the implications of such symmetries for the corresponding linear perturbation equations. We show that, in a spatially closed spacetime, the occurrence of a gauge symmetry implies a linearization instability in the linear perturbation problem. The perturbation equations must be supplemented by nonlinear constraints to exclude spurious solutions. The same phenomenon occurs in Minkowski space if one imposes the super-selection rule which constrains the conserved charges associated with the gauge symmetry genrators to remain fixed under the perturbation. Several examples involving spontaneous symmetry breaking are briefly discussed.