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Electron and hole self-energy contributions to the dynamic structure factor in interacting-electron systems.

A detailed investigation is made of the influence of particle self-energies on the dynamic response of the metallic electron gas. Two quite different approaches, the Green-Neilson-Szyma\ifmmode \acute{n}\else \'{n}\fi{}ski (GNS) theory and the quasiparticle-lifetime theory, are examined and contrasted. It is shown that the inclusion of off-shell effects in the quasiparticle-lifetime theory drastically alters its central conclusions. Moreover, that theory's neglect of cancellations between self-energy terms and other classes of terms seriously violates the major sum rules. These cancellations are closely connected with conservation principles. The GNS theory, being conserving, reproduces these cancellations in detail.