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

TL;DR

This paper introduces a unified theoretical framework for both equilibrium and nonequilibrium many-body perturbation theories, deriving various formalisms as special cases and providing a universal proof of Wick's theorem applicable across them.

Contribution

It unifies multiple many-body perturbation formalisms into a single framework based on the Martin-Schwinger hierarchy, including a generalized Wick theorem for arbitrary initial states.

Findings

Derivation of Keldysh, Matsubara, and zero-temperature formalisms as special cases

A universal proof of Wick's theorem valid for all formalisms

Extension of Wick's theorem to general initial states on the Keldysh contour

Abstract

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 many-body 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.