Electron Self-Energy and Generalized Drude Formula for Infrared Conductivity of Metals

Goetze and Woelfle (GW) wrote the conductivity in terms of a memory function M as (ine2/m)/(omega+M(omega)), where M=i/tau in the Drude limit. The analytic properties of -M are the same as those of the self-energy of a retarded Green's function. In the approximate treatment of GW, -M closely resembles a self-energy, with differences, e.g., the imaginary part is twice too large. The correct relation between -M and the self-energy is known for the electron-phonon case and is conjectured to be similar for other perturbations. When vertex corrections are ignored there is a known relation. A derivation using Matsubara temperature Green's functions is given.Comment: The original version (arXiv:cond-mat/0407777v1) of July 2004 has been slightly improved. It is now (July 2015) belatedly "in production" at Phys. Rev. B. This new version is the one which will appear in print. The referees made useful suggestions, and some more recent papers are now cited. There are 4 pages, 0 figure