Reducible Connections in Gauge Theories

When studying gauge theories (e.g. with finite energy conditions), attention is traditionally restricted to the subset of irreducible connections, which is open and dense in the full space of connections. We point out that generally the residual set of reducible connection contains critical points of the gauge functionals which, moreover, are the only ones common to all theories with a given symmetry, i.e. those determined by the symmetry and geometry of the problem alone, and not by the specific choice of functional.