  We consider the problem of removing the divergences in an arbitrary
gauge-field theory (possibly nonrenormalizable). We show that this can be
achieved by performing, order by order in the loop expansion, a redefinition of
some parameters (possibly infinitely many) and a canonical transformation (in
the sense of Batalin and Vilkovisky) of fields and BRS sources.
Gauge-invariance is turned into a suitable quantum generalization of
BRS-invariance. We define quantum observables and study their properties. We
apply the result to renormalizable gauge-field theories that are gauge-fixed
with a nonrenormalizable gauge-fixing and prove that their predictivity is
retained. A corollary is that topological field theories are predictive.
Analogies and differences with the formalisms of classical and quantum
mechanics are pointed out.
