Book contents
- Frontmatter
- Dedication
- Contents
- Author’s Note
- Part I Normal Phase
- 1 Introduction
- 2 The Schrödinger and Heisenberg Representations: Time-Evolution Operator
- 3 Splitting the Hamiltonian: Heisenberg and Interaction Pictures
- 4 Time-Dependent Quantum and Ensemble Averages: Initial Preparation of the System
- 5 Quantum Averages over the Ground State and the Gell–Mann–Low Theorem
- 6 The Contour Idea for Time-Dependent Averages: Forward and Backward Branches
- 7 Closed-Time-Path Green’s Functions
- 8 Dynamics for a Correlated Initial State and Various Kinds of Contours in the Complex Time Plane
- 9 Perturbation Theory: Wick’s Theorem for Strings of Operators Ordered along a Contour
- 10 Non-equilibrium Diagrammatics: Feynman Rules
- 11 Non-equilibrium Dyson Equations
- 12 Kubo–Martin–Schwinger Boundary Conditions
- 13 Converting Contour-Time to Real-Time Arguments
- 14 Langreth Rules: Convolutions and Products
- 15 The Kadanoff–Baym Equations
- 16 The t-Matrix Approximation in the Normal Phase
- 17 Contour Diagrammatic Structure in Terms of Functional Derivatives
- 18 Beyond Linear-Response Theory
- 19 Time-Dependent Hartree–Fock Approximation and Mean-Field Decoupling
- 20 Miscellany and Addenda to Part I
- Part II Fermionic Superfluid Phase
- Part III Applications
- Bibliography
- Index
7 - Closed-Time-Path Green’s Functions
from Part I - Normal Phase
Published online by Cambridge University Press: 06 February 2026
Book contents
- Frontmatter
- Dedication
- Contents
- Author’s Note
- Part I Normal Phase
- 1 Introduction
- 2 The Schrödinger and Heisenberg Representations: Time-Evolution Operator
- 3 Splitting the Hamiltonian: Heisenberg and Interaction Pictures
- 4 Time-Dependent Quantum and Ensemble Averages: Initial Preparation of the System
- 5 Quantum Averages over the Ground State and the Gell–Mann–Low Theorem
- 6 The Contour Idea for Time-Dependent Averages: Forward and Backward Branches
- 7 Closed-Time-Path Green’s Functions
- 8 Dynamics for a Correlated Initial State and Various Kinds of Contours in the Complex Time Plane
- 9 Perturbation Theory: Wick’s Theorem for Strings of Operators Ordered along a Contour
- 10 Non-equilibrium Diagrammatics: Feynman Rules
- 11 Non-equilibrium Dyson Equations
- 12 Kubo–Martin–Schwinger Boundary Conditions
- 13 Converting Contour-Time to Real-Time Arguments
- 14 Langreth Rules: Convolutions and Products
- 15 The Kadanoff–Baym Equations
- 16 The t-Matrix Approximation in the Normal Phase
- 17 Contour Diagrammatic Structure in Terms of Functional Derivatives
- 18 Beyond Linear-Response Theory
- 19 Time-Dependent Hartree–Fock Approximation and Mean-Field Decoupling
- 20 Miscellany and Addenda to Part I
- Part II Fermionic Superfluid Phase
- Part III Applications
- Bibliography
- Index
Summary
This chapter considers the product of operators in the Heisenberg representation and express it in terms of the contour time-ordering operator. Since the relative order in which the operators enter the quantum average matters, this order has to be specified in detail. This procedure leads to considering the single- and two-particle Green’s functions, where the product contains, respectively, two and four field operators, which are at the core of the diagrammatic many-particle theory to be developed in what follows.
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- Many-Body Green's Functions for Time-Dependent Problems , pp. 36 - 42Publisher: Cambridge University PressPrint publication year: 2026
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