  A method to implement the many-body Green function formalism in the GW
approximation for infinite non periodic systems is presented. It is suitable to
treat systems of known ``asymptotic'' properties which enter as boundary
conditions, while the effects of the lower symmetry are restricted to regions
of finite volume. For example, it can be applied to surfaces or localized
impurities. We illustrate the method with a study of the surface of
semi-infinite jellium. We report the dielectric function, the effective
potential and the electronic self-energy discussing the effects produced by the
screening and by the charge density profile near the surface.
