Book contents
- Frontmatter
- Contents
- Abbreviations and Frequent Notations
- Preface
- Part IPreliminaries
- Part IIEquilibrium
- 4Single-Particle Two-Time Green’s Functions
- 5Matsubara (Imaginary Time) Green’s Functions
- 6Feynman Diagrams for Matsubara Green’s Functions
- Part IIINon-equilibrium
- Part IVQuantum Transport Applications
- Appendix ANon-Hermitian Hamiltonian
- Appendix BAngular Momentum of an Electron
- Appendix CCanonical Transformation
- Appendix DThe Delta Function
- References
- Index
5 - Matsubara (Imaginary Time) Green’s Functions
from Part II - Equilibrium
Published online by Cambridge University Press: aN Invalid Date NaN
Book contents
- Frontmatter
- Contents
- Abbreviations and Frequent Notations
- Preface
- Part IPreliminaries
- Part IIEquilibrium
- 4Single-Particle Two-Time Green’s Functions
- 5Matsubara (Imaginary Time) Green’s Functions
- 6Feynman Diagrams for Matsubara Green’s Functions
- Part IIINon-equilibrium
- Part IVQuantum Transport Applications
- Appendix ANon-Hermitian Hamiltonian
- Appendix BAngular Momentum of an Electron
- Appendix CCanonical Transformation
- Appendix DThe Delta Function
- References
- Index
Summary
We first consider the one-particle Matsubara Green’s function, defined at two ‘imaginary’ times, and its properties, such as periodicity, expansion into a Fourier series, Lehmann representation and analytic continuation into the complex plane. Special attention is drawn to the technical point of calculating Matsubara series for both fermions and bosons. Then the Matsubara Green’s function is applied to study superconductivity within the BCS Hamiltonian. Consideration of interacting electrons leads to the notion of self-energy and the Dyson equation. Finally, the two-particle Matsubara Green’s function is introduced for different relations between its four times, and its Lehmann representation.
Keywords
Information
- Type
- Chapter
- Information
- Introduction to Green's Function Methods in Many-Body PhysicsWith Applications to Quantum Transport, pp. 211 - 248Publisher: Cambridge University PressPrint publication year: 2026
Accessibility standard: WCAG 2.2 A
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
The PDF of this chapter complies with version 2.2 of the
Web Content Accessibility Guidelines
(WCAG), offering more comprehensive accessibility measures for a broad range
of users and meets the basic
(A)
level of WCAG compliance, addressing essential accessibility barriers.
Content Navigation
Table of contents navigation
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Index navigation
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Reading Order & Textual Equivalents
Single logical reading order
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
Short alternative textual descriptions
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.