ABSTRACT
To a surprising extent, one can understand the elementary properties of metals in terms of noninteracting electrons and phonons-quantized lattice vibrations. For example, the low-temperature specific heat of a metal is the sum of a term linear in the temperature, T, from the electrons and a term proportional to T 3 from the phonons. This result follows from a noninteracting particle picture. The electrical conductivity limited by nonmagnetic impurity scattering is also well described by a noninteracting electron gas. In addition, from a knowledge of single-electron band theory, one can qualitatively discern the differences between metals, insulators, and semiconductors. The remarkable success of the noninteracting model is paradoxical because electrons and ions strongly interact both with themselves and with one another. Along with its successes, the noninteracting picture has colossal shortcomings, most notably its inability to describe old problems, such as cohesive energies, superconductivity, magnetism, and newer phenomena, such as the Kondo and fractional quantum Flail effects. We first review the physics of the noninteracting electron gas. It is only after we develop methodology for dealing with electron interactions that we can lay plain the reasons why the noninteracting model works so well.
