## Nonequilibrium Many-Body Theory of Quantum Systems: A Modern IntroductionThe Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics. |

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### Contents

model Hamiltonians 339 | 39 |

Timedependent problems and equations of motion | 81 |

The contour idea | 95 |

Manyparticle Greens functions | 125 |

Oneparticle Greens function | 153 |

Mean ﬁeld approximations | 205 |

twoparticle Greens function | 235 |

selfenergy | 249 |

MBPT for the twoparticle Greens function | 323 |

Applications of MBPT to equilibrium problems | 347 |

preliminaries | 385 |

manybody formulation | 407 |

Applications of MBPT to nonequilibrium problems | 455 |

From the N roots of to the Dirac 6function | 503 |

KramersKronig relations | 582 |

593 | |

MBPT for the Greens function | 275 |

MBPT and variational principles for the grand potential | 295 |

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### Common terms and phrases

atomic bosons boundary conditions calculate chemical potential coefﬁcients component conﬁguration consider continuum contour correlation deﬁne deﬁnition density matrix depends derivative diagrammatic Dyson equation eigenkets eigenstates eigenvalues electron gas energy ensemble average equations of motion equilibrium excitations expansion Fermi fermions ﬁeld operators ﬁgure ﬁnd ﬁnding ﬁnite ﬁrst ﬁrst order ﬁrst term formula Fourier transform frequency fulﬁll grand potential Green's function Green’s Hamiltonian Hartree—Fock approximation Heisenberg picture hence identity inﬁnitely inﬁnitesimal initial Inserting integral interaction lines linear response many-body Martin—Schwinger hierarchy matrix elements Matsubara MBPT molecule momentum noninteracting number of particles obtained one-particle permanent/determinant permutation permutation graph perturbation physical plasmon position—spin potential prefactor quantity quantization quantum number relation response function result rewrite satisﬁes Section self-energy self-energy diagrams single-particle solution spectral function spin symmetry Taking into account theorem time-dependent two-particle vacuum diagram vanishes vector vertical track wavefunction WBLA zero temperature