Abstract

Abstract This chapter considers two methods designed for calculating the real-time (retarded, advanced, and Keldysh) Green functions of nonstationary superconductors: (i) the method of analytical continuation worked out by Eliashberg; and (ii) the Keldysh diagram technique. The Eliashberg phonon model of superconductivity is discussed and the equation for the order parameter is derived. Expressions for self-energies of electron-phonon and electron-electron interactions are obtained. Transport-like equations for the retarded (advanced) and Keldysh Green functions of particles interacting with impurities, phonons, and with each other are derived. Expressions for the electron density, electric current, internal energy, and energy current are derived in terms of the Keldysh Green functions.

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