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.
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