Properties and Use of the Green’s Functions

  • Eleftherios N. Economou
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 7)


The Green’s functions defined in Chap.8 have similar but not identical analytical properties as the Green’s functions defined in Chap.2 corresponding to second-order (in time) differential equations. They can all be expressed in terms of a generalized DOS and the Fermi or Bose thermal equilibrium distributions. From the Green’s functions (or the generalized DOS) one can easily obtain all thermodynamic quantities and linear response functions, like the conductivity. The poles of an appropriate analytic continuation of G in the complex E-plane can be interpreted as the energy (the real part of the pole) and the inverse life time (the imaginary part of the pole) of quasi-particles. The latter are entities which allow us to map an interacting system to a noninteracting one.


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  1. 9.1
    A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski: Methods of Quantum Field Theory in Statistical Physics ( Prentice Hall, Englewood Cliffs, NJ 1963 )MATHGoogle Scholar
  2. 9.2
    L.P. Kadanoff, G. Baym: Quantum Statistical Mechanics (Benjamin, New York 1962 )Google Scholar
  3. 9.3
    P. Nozieres: Theory of Interacting Fermi Systems (Benjamin, New York 1964 )Google Scholar
  4. 9.4
    S. Doniach, E.H. Sondheimer: Green’s Functions for Solid State Physicists (Benjamin, Reading, Mass. 1974 )Google Scholar
  5. 9.5
    R.D. Mattuck: A Guide to Feynman Diagrams in the Many-Body Problem ( McGraw-Hill, New York 1967 )Google Scholar
  6. 9.6
    L.D. Landau, E.M. Lifshitz: Statistical Physics (Pergamon Press, London 1959) pp.39 and 70Google Scholar
  7. 9.7
    See, e.g., R. Kubo: J. Phys. Soc. Jap. 12, 570 (1957); K.M. Case: Transp. Th. Stat. Phys. 2, 129 (1972)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Eleftherios N. Economou
    • 1
  1. 1.Department of PhysicsUniversity of CreteHeraklion, CreteGreece

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