As we have seen in the previous chapters, interactions, if they are not too strong, preserve many features of the electronic system which are present in the noninteracting case (Fermi gas, Chapter 7). In general, however, the interactions are not at all small: for instance in typical metals, rs ∼ 2–3, and not rs « 1 as was implicitly assumed in Chapter 9 and which was actually the condition for the applicability of perturbation theory used there. Nevertheless we know that the description of normal metals using the concepts developed for the free Fermi gas or Fermi systems with weak interactions (such asDrude theory, for example) is very successful.

An explanation of the success of the conventional theory of metals, and the generalization of the corresponding description to a more general situation, was given by Landau in his theory of Fermi liquids. This theory is very important conceptually, although in the usual metals there are only few special effects which indeed require this treatment. However, there exist also systems (3He, or rare earth systems with mixed valence and heavy fermions) for which this approach is really vital. Also the emerging new field of non-Fermi-liquid metallic systems requires first an understanding of what is the normal Fermi liquid.

The foundations of the Fermi-liquid theory

Themain assumptions of the Landau Fermi liquid theory are completely in linewith our general approach.