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16 pages, 5 figuresMotivated 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 Λ affecting only the on-shell prescription of the free (abelian) gluon propagator. When summed to all orders in gΛ the modification is equivalent to evaluating standard Green functions in a pure gauge field with an imaginary gauge parameter ∝Λ. We show how to calculate the corresponding dressed Green functions, which are Poincaré and gauge covariant. We evaluate the expressions for the dressed quark and qqˉ propagators, imposing as boundary condition that they approach the standard perturbative form in the short-distance limit (∣p2∣→∞). The on-shell (p2=m2) pole of the free quark propagator is removed for any Λ>0, and replaced by a discontinuity which vanishes exponentially with p2. 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
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