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15 - Green Functions for Many-Body Systems and Feynman Diagrams
from Part Three - Many-Body Physics
Michael El-Batanouny, Boston University
Book:

Advanced Quantum Condensed Matter Physics

Published online:

06 March 2020

Print publication:

26 March 2020, pp 425-517
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Summary

Develops the many-body one-particle Green function, and explains its physical interpretation in terms of the spectral function, self-energy, and quasiparticle. lifetime. Its application in angle-resolved photoemission spectroscopy is presented in detail. The time-evolution operator in the interaction picture is derived, and time-ordering and adiabatic switching-on are introduced as precursor tools to construct the Feynman–Dyson many-body perturbation theory. A detailed account of Wick’s theorem, normal ordering, and contractions is outlined. Feynman diagrams are constructed, and the emergence of the infinite Dyson series from irreducible diagrams is outlined. Two-particle Green function and the particle-hole excitation spectra are developed. Diagramatic application of RPA for interacting systems is described. The finite-temperature Matsubara Green function is introduced and developed, together with its Fourier series representation and the evaluation of Matsubara sums.