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We present a unified framework for equilibrium and nonequilibrium many-bodyperturbation theory. The most general nonequilibrium many-body theory valid forgeneral initial states is based on a time-contour originally introduced byKonstantinov and Perel'. The various other well-known formalisms of Keldysh,Matsubara and the zero-temperature formalism are then derived as special casesthat arise under different assumptions. We further present a single simpleproof of Wick's theorem that is at the same time valid in all these flavors ofmany-body theory. It arises simply as a solution of the equations of theMartin-Schwinger hierarchy for the noninteracting many-particle Green'sfunction with appropriate boundary conditions. We further discuss a generalizedWick theorem for general initial states on the Keldysh contour and derive howthe formalisms based on the Keldysh and Konstantinov-Perel'-contours arerelated for the case of general initial states.

Equilibrium and nonequilibrium many-body perturbation theory: a unified framework based on the Martin-Schwinger hierarchy