"When certain materials are cooled below a certain critical temperature Tc, they suddenly become superconducting. Historically, physicists had long suspected that the superconducting transition, just like the superfluid transition, has something to do with Bose-Einstein condensation. But electrons are fermions, not bosons, and thus they first have to pair into bosons, which then condense. We now know that this general picture is substantially correct: Electrons form Cooper pairs, whose condensation is responsible for superconductivity. With brilliant insight, Landau and Ginzburg realized that without having to know the detailed mechanism driving the pairing of electrons into bosons, they could understand a great deal about superconductivity by studying the field φ(x) associated with these condensing bosons. In analogy with the ferromagnetic transition in which the magnetization M⃗(x) in a ferromagnet suddenly changes from zero to a nonzero value when the temperature drops below some critical temperature, they proposed that φ(x) becomes nonzero for temperatures below Tc. (In this chapter x denotes spatial coordinates only.) In statistical physics, quantities such as M⃗(x) and φ(x) that change through a phase transition are known as order parameters. The field φ(x) carries two units of electric charge and is therefore complex."