Abstract
AbstractThe on‐shell self‐energy of the homogeneous electron gas in second order of exchange, Σ2x = Re Σ2x (kF, k2 F/2), is given by a certain integral. This integral is treated here in a similar way as Onsager, Mittag, and Stephen [Ann. Physik (Leipzig) 18, 71 (1966)] have obtained their famous analytical expression e2x = (in atomic units) for the correlation energy in second order of exchange. Here it is shown that the result for the corresponding on‐shell self‐energy is Σ2x = e2x. The off‐shell self‐energy Σ2x (k, o) correctly yields 2e2x (the potential component of e2x) through the Galitskii‐Migdal formula. The quantities e2x and Σ2x appear in the high‐density limit of the Hugenholtz‐van Hove (Luttinger‐Ward) theorem.
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