Quantum Theory of Many-Body Systems pp 53-100 | Cite as

# Green’s Functions at Zero Temperature

Chapter

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## Abstract

Green’s functions as a tool for probing the response of a many-body system to an external perturbation. Similarity and difference from a one-particle propagator. Statistical ensembles. Definition of Green’s functions at zero temperature. Analytical properties of Green’s functions and their relation to quasiparticles. Perturbation theory and diagram techniques for Green’s functions at zero temperature. "Dressing" of particles and interactions: Polarization operator and self energy. Many-particle Green’s functions.

## References

## Book and Reviews

- 1.Abrikosov, A.A., Gorkov, L.P., Dzyaloshinski, I.E.: Methods of quantum field theory in statistical physics. Ch. 2. Dover Publications, New York (1975) (An evergreen classic on the subject.)Google Scholar
- 2.Fetter, A.L., Walecka, J.D.: Quantum theory of many-particle systems. McGraw-Hill, San Francisco (1971)Google Scholar
- 3.Mahan, G.D.: Many-particle physics. Plenum Press, New York (1990) ([2] and [3] are high-level, very detailed monographs: the standard references on the subject.)Google Scholar
- 4.Lifshitz, E.M., Pitaevskii, L.P.: Statistical physics pt. II. (Landau and Lifshitz Course of theoretical physics, v. IX.) Pergamon Press, New York (1980) (Ch. 2. A comprehensive, but very compressed account of the zero-temperature Green’s functions techniques.)Google Scholar
- 5.Mattuck, R.: A guide to Feynman diagrams in the many-body problem. McGraw-Hill, New York (1976) (Green’s functions techniques are presented in a very instructive and intuitive way.)Google Scholar
- 6.Nussenzvejg, H.M.: Causality and dispersion relations. Academic Press, New York (1972). (A very good book for the mathematically inclined reader)Google Scholar
- 7.Thouless, D.J.: Quantum mechanics of many-body systems. Academic Press, New York (1972)Google Scholar
- 8.Ziman, J.M.: Elements of advanced quantum theory. Ch. 3, 4. Cambridge University Press, Cambridge (1969)Google Scholar

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