  We develop a general field-covariant approach to quantum gauge theories.
Extending the usual set of integrated fields and external sources to "proper"
fields and sources, which include partners of the composite fields, we define
the master functional Omega, which collects one-particle irreducible diagrams
and upgrades the usual Gamma-functional in several respects. The functional
Omega is determined from its classical limit applying the usual diagrammatic
rules to the proper fields. Moreover, it behaves as a scalar under the most
general perturbative field redefinitions, which can be expressed as linear
transformations of the proper fields. We extend the Batalin-Vilkovisky
formalism and the master equation. The master functional satisfies the extended
master equation and behaves as a scalar under canonical transformations. The
most general perturbative field redefinitions and changes of gauge-fixing can
be encoded in proper canonical transformations, which are linear and do not mix
integrated fields and external sources. Therefore, they can be applied as true
changes of variables in the functional integral, instead of mere replacements
of integrands. This property overcomes a major difficulty of the functional
Gamma. Finally, the new approach allows us to prove the renormalizability of
gauge theories in a general field-covariant setting. We generalize known
cohomological theorems to the master functional and show that when there are no
gauge anomalies all divergences can be subtracted by means of parameter
redefinitions and proper canonical transformations.
