Quantum Gauge Symmetry from Classical Gauge Non-invariant Action

We have recently shown that the modified quantization scheme of Zwanziger, Parrinello and Jona-Lasinio is in fact identical at least in the perturbative accuracy to the conventional Faddeev-Popov formula, if one takes into account the variation of the gauge field along the entire gauge orbit. This in particular suggests that the classical massive gauge theory, for example, and the gauge invariant theory, whose gauge symmetry is broken by a gauge fixing term, have no intrinsic differences in a suitably quantized theory. Classical gauge symmetry is sufficient to ensure quantum gauge symmetry (BRST symmetry), but it is not necessary in general. It is thus suggested to extend the notion of quantum gauge symmetry not only to classical gauge theory but also to any theory whose gauge symmetry is broken by some extra terms in the classical action. As for massive gauge particles, only the Higgs mechanics, where the mass term is gauge invariant, has an intrinsic meaning. We comment on a possible connection of the present observation to the past arguments against the dynamical generation of massless gauge fields. 1