Summary
The Green’s functions defined in Chap. 10 have analytical properties that are similar but not identical to 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 lifetime (the imaginary part of the pole) of quasiparticles. The latter are entities that allow us to map an interacting system to a noninteracting one.
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Chapter 11
R. D. Mattuck. A Guide to Feynman Diagrams in the Many-Body Problem. McGraw-Hill, New York, second edition, 1976.
L. D. Landau and E. M. Lifshitz. Statistical Physics, pages 39, 70. Pergamon, London, first edition, 1959.
Philippe Nozieres. Theory of Interacting Fermi Systems. Benjamin, New York, 1964.
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© 2006 Springer-Verlag Berlin Heidelberg
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(2006). Properties and Use of the Green’s Functions. In: Green’s Functions in Quantum Physics. Springer Series in Solid-State Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28841-4_11
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DOI: https://doi.org/10.1007/3-540-28841-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28838-1
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