Higgs phenomenon without symmetry breaking order parameter

We discuss symmetry-breaking order parameters, e.g. , in gauge theories with Higgs scalars, phi, in suitable gauges. We show that, typically, = 0. A complete set of gauge-invariant, observable composite fields for such theories, local ones and ones localized near strings (paths) is constructed. We then examine the validity of standard perturbation theory, based on assuming that not equal 0, and reformulate it in terms of our gauge-invariant fields and without assuming that not equal 0. Finally, we classify classical field configurations with non-trivial topology ('defects') in such theories and propose a defect-gas approach to predict their effects. (orig.)