格林函数是解决物理学问题最强大和最通用的方法之一，其中的非平衡态理论对许多研究领域的影响更是不可估量的。本书自成体系，全面论述了非平衡态多体理论。作者从量子力学入手，阐述了平衡态和非平衡态格林函数形式，轮廓格林函数和图解展开式的物理内涵，介绍了这些理论在从分子、纳米结构到金属和绝缘体等诸多领域的应用。本书适用于物理及相关专业的研究生和科研工作者。

Preface
List of abbreviations and acronyms
Fundamental constants and basic relations
1 Second quantization
1.1 Quantum mechanics of one particle
1.2 Quantum mechanics of many particles
1.3 Quantum mechanics of many identical particles
1.4 Field operators
1.5 General basis states
1.6 Hamiltonian in second quantization
1.7 Density matrices and quantum averages
2 Getting familiar with second quantization: model Hamiltonians
2.1 Model Hamiltonians
2.2 Pariser-Parr-Pople model
2.3 Noninteracting models
2.3.1 Bloch theorem and band structure
2.3.2 Fano model
2.4 Hubbard model
2.4.1 Particle-hole symmetry: application to the Hubbard dimer
2.5 Heisenberg model
2.6 BCS model and the exact Richardson solution
2.7 Holstein model
2.7.1 Peierls instability
2.7.2 Lang-Firsov transformation: the heavy polaron
3 Time-dependent problems and equations of motion
3.1 Introduction
3.2 Evolution operator
3.3 Equations of motion for operators in the Heisenberg picture
3.4 Continuity equation: paramagnetic and diamagnetic currents
3.5 Lorentz Force
4 The contour idea
4.1 Time-dependent quantum averages
4.2 Time-dependent ensemble averages
4.3 Initial equilibrium and adiabatic switching
4.4 Equations of motion on the contour
4.5 Operator correlators on the contour
5 Many-particle Green's functions
5.1 Martin-Schwinger hierarchy
5.2 Truncation of the hierarchy
5.3 Exact solution of the hierarchy from Wick's theorem
5.4 Finite and zero-temperature formalism from the exact solution
5.5 Langreth rules
6 One-particle Green's function
6.1 What can we learn from G?
6.1.1 The inevitable emergence of memory
6.1.2 Matsubara Green's function and initial preparations
6.1.3 Lesser/greater Green's function: relaxation and quasi-particles
6.2 Noninteracting Green's function
6.2.1 Matsubara component
6.2.2 Lesser and greater components
6.2.3 All other components and a useful exercise
6.3 Interacting Green's function and Lehmann representation
6.3.1 Steady-states, persistent oscillations, initial-state dependence
6.3.2 Fluctuation-dissipation theorem and other exact properties
6.3.3 Spectral function and probability interpretation
6.3.4 Photoemission experiments and interaction effects
6.4 Total energy from the Galitskii-Migdal formula
7 Mean field approximations
7.1 Introduction
7.2 Hartree approximation
7.2.1 Hartree equations
7.2.2 Electron gas
7.2.3 Quantum discharge of a capacitor
7.3 Hartree-Fock approximation
7.3.1 Hartree-Fock equations
7.3.2 Coulombic electron gas and spin-polarized solutions
8 Conserving approximations: two-particle Green's function
8.1 Introduction
8.2 Conditions on the approximate G2
8.3 Continuity equation
8.4 Momentumconservation law
8.5 Angular momentum conservation law
8.6 Energy conservation law
9 Conserving approximations: self-energy
9.1 Self-energy and Dyson equations I
9.2 Conditions on the approximate Σ
9.3 φ functional
9.4 Kadanoff-Baym equations
9.5 Fluctuation-dissipation theorem for the self-energy
9.6 Recovering equilibrium from the Kadanoff-Baym equations
9.7 Formal solution of the Kadanoff-Baym equations
10 MBPT for the Green's function
10.1 Getting started with Feynman diagrams
10.2 Loop rule
10.3 Cancellation of disconnected diagrams
10.4 Summing only the topologically inequivalent diagrams
10.5 Self-energy and Dyson equations II
10.6 G-skeleton diagrams
10.7 W-skeleton diagrams
10.8 Summary