  Motivated by the gluon condensate in QCD we study the perturbative expansion
of a gauge theory in the presence of gauge bosons of vanishing momentum, in the
specific case of an abelian theory. The background is characterised by a
dimensionful parameter $\Lambda$ affecting only the on-shell prescription of
the free (abelian) gluon propagator. When summed to all orders in $g\Lambda$
the modification is equivalent to evaluating standard Green functions in a pure
gauge field with an imaginary gauge parameter $\propto \Lambda$. We show how to
calculate the corresponding dressed Green functions, which are Poincare and
gauge covariant. We evaluate the expressions for the dressed quark and $q \bar
q$ propagators, imposing as boundary condition that they approach the standard
perturbative form in the short-distance limit ($|p^2|\to\infty$). The on-shell
($p^2=m^2$) pole of the free quark propagator is removed for any $\Lambda > 0$,
and replaced by a discontinuity which vanishes exponentially with $p^2$. The
dressing introduces an effective interaction between quarks and antiquarks
which is enhanced at low relative 3-momentum. Further study should allow to
identify the (bound) eigenstates of propagation and determine whether they
define a unitary S-matrix. When the quark mass is zero there is a euclidean
propagator solution which breaks chiral symmetry spontaneously. We study some
aspects of the massless pion contribution to axial vector correlators and
derive the $\pi q \bar q$ form factor.
