Applicability of the local field concept for the electron gas

The static exchange-correlation hole surrounding an electron in an electron gas at metallic densities has been a highly successful and useful concept. The properties of the static exchange-correlation hole can be accurately reflected by the construction of a static local field. This field surrounds each electron and modifies it interaction with the other electrons in the system. An important limitation of the local field concept is that it does not handle the time-dependent relaxation of the surrounding electron cloud in a particularly transparent way. At metallic densities this is if no consequence since relaxation effects are only small corrections anyway, but at lower densities and in two-dimensional systems they become increasingly important. Approaches which attempt to address these problems are discussed. (author). 12 refs, 4 figs