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.
Men say that the Bodhisat Himself drew it with grains of rice upon dust, to teach His disciples the cause of things. Many ages have crystallised it into a most wonderful convention crowded with hundreds of little figures whose every line carries a meaning.
Rudyard Kipling. “Kim.”
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
It can be shown that no matter what the spin of real fermions, the (basic) quasiparticles will have spin 1/2 (though there will be several types of quasiparticles); see [4, §1).
- 2.
Of course, this equation can as well be written for the two–particle Green’s function itself, instead of the vertex function.
References
Book and Reviews
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.)
Fetter, A.L., Walecka, J.D.: Quantum theory of many-particle systems. McGraw-Hill, San Francisco (1971)
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.)
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.)
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.)
Nussenzvejg, H.M.: Causality and dispersion relations. Academic Press, New York (1972). (A very good book for the mathematically inclined reader)
Thouless, D.J.: Quantum mechanics of many-body systems. Academic Press, New York (1972)
Ziman, J.M.: Elements of advanced quantum theory. Ch. 3, 4. Cambridge University Press, Cambridge (1969)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Zagoskin, A. (2014). Green’s Functions at Zero Temperature. In: Quantum Theory of Many-Body Systems. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-07049-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-07049-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07048-3
Online ISBN: 978-3-319-07049-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)