Many-Body Perturbation Theory

Abstract

The electrons in atoms, molecules and solids as characterised by the Hamilto-nian (2.1) constitute an inhomogeneous electron gas. A classical tool for the discussion of the inhomogeneous electron gas is the diagrammatic approach of many-body perturbation theory (see, e.g., Hedin and Lundqvist, 1969; Fetter and Walecka, 1971; Mahan, 1981). Due to the mathematical complexity of the problem at hand, most explicit results obtained by many-body perturbation theory refer to the homogeneous electron gas and its linear response to external perturbations. Progress in the treatment of fully inhomogeneous systems beyond linear response has been reported only recently (for finite systems see, e.g., von Niessen, Cederbaum, and Domcke, 1978; Schirmer, Cederbaum, and Walter, 1983; for extended systems see, e.g., Hybertsen and Louie, 1985 a, b, 1986; Godby, Schlüter, and Sham, 1986, 1987 a, b; von der Linden and Horsch, 1988).