REDUCIBLE CONNECTIONS IN GAUGE-THEORIES

When studying gauge theories (e.g. with finite energy conditions), att ention is traditionally restricted to the subset of irreducible connec tions, which is open and dense in the full space of connections. We po int out that generally the residual set of reducible connections conta ins critical points of the gauge functionals which, moreover, are the only ones common to all theories with a given symmetry, i.e. those det ermined by the symmetry and geometry of the problem alone, and not by the specific choice of functional.