  A particular difficulty in studying many-body interactions in a solid is the
absence of an experimental technique that can directly probe their key
characteristics. We show that 2D Fourier spectroscopy provides an efficient
tool for the measurement of critical parameters describing the effect of
many-body interactions on the optical response of semiconductors. We develop
the basic microscopic theory of 2D Fourier spectroscopy of semiconductors in
the framework of the three-band model (heavy holes, light holes, and
electrons). The theory includes many-body correlations nonperturbatively and
can be generalized straightforwardly in order to describe 2D Fourier spectra
obtained in atomic physics. We establish a relation between the 2D Fourier
spectrum and the many-body correlations. It is shown, in particular, that 2D
Fourier spectroscopy provides a principal possibility to establish
experimentally the origin of the fast decay of the memory term describing the
Coulomb interaction between heavy- and light-hole excitons. The theory is
applied to an analysis of the available experimental data. Experiments
providing more detailed information are suggested.
