Abstract
Using the Green function formalism an expression for the dielectric response function (or density-density function) is derived which is of second order with respect to the Coulomb interaction and applies for arbitrary wave vector and frequency. The employed procedure is somehow lengthy but quite clear from the mathematical point of view. Decoupling methods for Green functions are not used. The theory contains the well-known expressions of the HFA, RPA and the first-order local field theory. In addition to this all four-particle processes (two electrons and two holes) are taken into account and represented in a closed formula, which is the four-particle analog to the Lindhard function. As a first application the plasmon damping is investigated.
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Gasser, W. Second-order theory of the dielectric response function of the electron gas. Z. Physik B - Condensed Matter 57, 15–22 (1984). https://doi.org/10.1007/BF01679921
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DOI: https://doi.org/10.1007/BF01679921