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
4 - Single-Particle Two-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
Various Green’s functions between any two operators at non-zero temperature are introduced (retarded, advanced, greater, lesser and causal), and their properties are investigated, such as fluctuation–dissipation theorem, Lehmann representation and continuation into the complex plane. We introduce the concept of quasiparticles from the spectral function. The method of the hierarchy of the equations of motion for Green’s functions of increasing complexity is illustrated on the Anderson model of a magnetic impurity. Finally, we study the magnetisation of a ferromagnet using spin–spin Green’s functions within the mean-field approximation.
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- Information
- Introduction to Green's Function Methods in Many-Body PhysicsWith Applications to Quantum Transport, pp. 167 - 210Publisher: Cambridge University PressPrint publication year: 2026
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