  The implementation of the Background Field Method (BFM) for quantum field
theories is analysed within the Batalin-Vilkovisky (BV) formalism. We provide a
systematic way of constructing general splittings of the fields into classical
and quantum parts, such that the background transformations of the quantum
fields are linear in the quantum variables. This leads to linear Ward-Takahashi
identities for the background invariance and to great simplifications in
multiloop computations. In addition, the gauge fixing is obtained by means of
(anti)canonical transformations generated by the gauge-fixing fermion. Within
this framework we derive the BFM for the N=2 Super-Yang-Mills theory in the
Wess-Zumino gauge viewed as the twisted version of Donaldson-Witten topological
gauge theory. We obtain the background transformations for the full BRST
differential of N=2 Super-Yang-Mills (including gauge transformations, SUSY
transformations and translations). The BFM permits all observables of the
supersymmetric theory to be identified easily by computing the equivariant
cohomology of the topological theory. These results should be regarded as a
step towards the construction of a super BFM for the Minimal Supersymmetric
Standard Model.
