QCD Green functions in a gluon field

21 pages, 7 figures. Minor modifications in text. Version to be published in JHEPWe formulate a dressed perturbative expansion of QCD, where the standard diagrams are evaluated in the presence of a constant external gluon field whose magnitude is gaussian distributed. The approach is Poincar{é} and gauge invariant, and modifies the usual results for hard processes only by power suppressed contributions. Long distance propagation of quarks and gluons turns out to be inhibited due to a branch point singularity instead of a pole at $p^2=0$ in the quark and gluon propagators. The dressing keeps the (massless) quarks in q qbar fluctuations of the photon at a finite distance from each other