  The use of the mass term as a gauge fixing term has been studied by
Zwanziger, Parrinello and Jona-Lasinio, which is related to the non-linear
gauge $A_{\mu}^{2}=\lambda$ of Dirac and Nambu in the large mass limit. We have
recently shown that this modified quantization scheme is in fact identical to
the conventional {\em local} Faddeev-Popov formula {\em without} taking the
large mass limit, if one takes into account the variation of the gauge field
along the entire gauge orbit and if the Gribov complications can be ignored.
This suggests that the classical massive vector theory, for example, is
interpreted in a more flexible manner either as a gauge invariant theory with a
gauge fixing term added, or as a conventional massive non-gauge theory. As for
massive gauge particles, the Higgs mechanics, where the mass term is gauge
invariant, has a more intrinsic meaning.
  It is suggested to extend the notion of quantum gauge symmetry (BRST
symmetry) not only to classical gauge theory but also to a wider class of
theories whose gauge symmetry is broken by some extra terms in the classical
action. We comment on the implications of this extended notion of quantum gauge
symmetry.
