  We show that in Yang-Mills theory the Slavnov-Taylor (ST) identity, extended
in the presence of a background gauge connection, allows to fix in a unique way
the dependence of the vertex functional on the background, once the 1-PI
amplitudes at zero background are known. The reconstruction of the background
dependence is carried out by purely algebraic techniques and therefore can be
applied in a non-perturbative scheme (e.g. on the lattice or in the
Schwinger-Dyson approach), provided that the latter preserves the ST identity.
The field-antifield redefinition, which replaces the classical
background-quantum splitting when quantum corrections are taken into account,
is considered on the example of an instanton background in SU(2) Yang-Mills
theory.
