Equilibrium and nonequilibrium many-body perturbation theory: a unified framework based on the Martin-Schwinger hierarchy
van Leeuwen, R., & Stefanucci, G. (2013). Equilibrium and nonequilibrium many-body perturbation theory: a unified framework based on the Martin-Schwinger hierarchy. In Progress in Nonequilibrium Green's Functions V (PNGF V), 27–31 August 2012, Jyväskylä, Finland (pp. 012001). Journal of Physics: Conference Series (427). Bristol: Institute of Physics. doi:10.1088/1742-6596/427/1/012001
Published inJournal of Physics: Conference Series;427
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We present a unified framework for equilibrium and nonequilibrium many-body perturbation theory. The most general nonequilibrium many-body theory valid for general initial states is based on a time-contour originally introduced by Konstantinov and Perel’. The various other well-known formalisms of Keldysh, Matsubara and the zero-temperature formalism are then derived as special cases that arise under different assumptions. We further present a single simple proof of Wick’s theorem that is at the same time valid in all these flavors of manybody theory. It arises simply as a solution of the equations of the Martin-Schwinger hierarchy for the noninteracting many-particle Green’s function with appropriate boundary conditions. We further discuss a generalized Wick theorem for general initial states on the Keldysh contour and derive how the formalisms based on the Keldysh and Konstantinov-Perel’-contours are related for the case of general initial states.