Single particle versus collective electronic excitations

As a first approximation, a metal can be modelled as an electron gas. A non-interacting electron gas has a continuous spectrum of electron-hole pair excitations. At each wavevector Q with |Q| less than the maximum Fermi surface spanning vector (2kF) there is a continuous set of electron-hole pair states, with a maximum energy but no gap (the minimum energy is zero.) Once the Coulomb interaction is taken into account, a new collective mode, the plasmon, is built from the electron-hole pair spectrum. The plasmon captures most of the spectral weight in the scattering cross-section, yet the particle-hole pairs remain practically unchanged, as can be seen from the success of the Landau Fermi-liquid picture. This article explores how even an isolated electron-hole pair in non-interacting approximation is a form of charge density wave excitation, and how the Coulomb interaction totally alters the charge properties, without affecting many other properties of the electron-hole pairs.