*
F. Aryasetiawan and O. Gunnarsson
Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
*

Calculations of
ground-state and excited-state properties of materials have been
one of the major goals of condensed matter physics. Ground-state properties
of solids
have been extensively investigated for several decades
within the standard density functional theory.
Excited state properties, on the other hand,
were relatively unexplored in *ab initio* calculations
until a decade ago.
The most suitable approach up to now for studying excited-state properties
of extended systems is the Green function method.
To calculate the Green function one requires the self-energy operator which
is non-local and energy dependent. In this article we describe the *GW*
approximation which has turned out to be
a fruitful approximation to the self-energy.
The Green function theory,
numerical methods for carrying out the self-energy calculations, simplified
schemes, and
applications to various systems are described.
Self-consistency issue and new developments beyond the
*GW* approximation are also discussed as well as
the success and shortcomings of the *GW* approximation.

Rep. Prog. Phys. ** 61 **, 237 (1998).

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