It is quite beyond the purpose of this book to give a comprehensive review of the modern theory of metals. I shall touch only on those topics which are related to the mainstream of this course: the problem of strong interactions. As I have noted before, strong interactions can appear as a result of renormalization, and from the aesthetic point of view this is, perhaps, the most interesting case. As we shall see in Part IV, such renormalizations are particularly strong in one-dimensional systems, where practically any interaction leads to quite dramatic effects. Therefore a one-dimensional electron gas neither undergoes a phase transition (this is forbidden due to the low dimensionality), nor behaves like a system of free electrons. On the contrary, in higher dimensions at low temperatures a system of electrons either undergoes a phase transition (superconductivity, magnetic ordering, etc.), or behaves like a free electron gas.

When temperatures as low as several degrees became experimentally available, physicists discovered that an enormous amount of experimental data on normal metals can be described by the model where one neglects electron–electron interactions. This apparent miracle was explained by Landau who demonstrated that the interaction pattern drastically simplifies close to the Fermi surface. Provided the system does not undergo a symmetry breaking phase transition, all interactions except forward scattering effectively vanish on the Fermi surface and low-lying excitations carry quantum numbers of electrons. Therefore they are called quasi-particles. The meaning of the word quasi will become clear in a moment.