On the nonequilibrium diagram technique: derivation, some features, and applications

We review the succession of ideas underlying the emergence of the nonequilibrium diagram technique (Keldysh diagram technique). Simple examples are used to illustrate the implementation of the technique and to demonstrate possible difficulties and the ways to overcome them. Together with well-known facts, some lesser-discussed details are considered, in particular, whether the so-called three-component technique is necessary. Several applications of the nonequilibrium diagram technique are discussed including, notably, tunneling systems and linear response problems. We hope that some parts of the review can be useful even for the reader familiar with the nonequilibrium diagram technique.