@inbook{18606,
  abstract     = {{In this lecture we present many-body perturbation theory as a method to determine quasiparticle excitations in solids, especially electronic band structures, accurately from first principles. The main ingredient is the electronic self-energy that, in principle, contains all many-body exchange and correlation effects beyond the Hartree potential. As its exact mathematical expression is unknown, approximations must be used in practical calculations. The approximation is obtained using a systematic algebraic approach on the basis of Green function techniques. It constitutes an expansion of the self-energy up to linear order in the screened Coulomb potential, which describes the interaction between the quasiparticles and includes dynamic screening through the creation of exchange-correlation holes around the bare particles. The implementation of the approximation relies on a perturbative treatment starting from density functional theory. Besides a detailed mathematical discussion we focus on the underlying physical concepts and show some illustrative applications.}},
  author       = {{Friedrich, Christoph and Schindlmayr, Arno}},
  booktitle    = {{Computational Nanoscience: Do It Yourself!}},
  editor       = {{Grotendorst, Johannes and Blügel, Stefan and Marx, Dominik}},
  isbn         = {{3-00-017350-1}},
  location     = {{Jülich}},
  pages        = {{335--355}},
  publisher    = {{John von Neumann Institute for Computing}},
  title        = {{{Many-body perturbation theory: The GW approximation}}},
  volume       = {{31}},
  year         = {{2006}},
}