Mathematical Diffraction Theory

A Glimpse at Mathematical Diffraction Theory

Mathematical diffraction theory is concerned with the analysis of the diffraction measure of a translation bounded complex measure ω. It emerges as the Fourier transform of the autocorrelation measure of ω. The mathematically rigorous approach has produced a number of interesting results in the context of perfect and random systems, some of which are summarized here.

Mathematical diffraction of aperiodic structures.

Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of matter, beyond perfect crystals, lead to pure point diffraction, hence to sharp Bragg peaks only. More recently, it has become apparent that one also has to stu...

Diffraction Theory

Geometrical theory of diffraction.

QCD, diffraction and string theory

Recently, string theory on some specific curved backgroud spacetime geometries has been conjectured to be equivalent to certain gauge theories (AdS/CFT correspondence). This correspondence may be used to investigate the non-perturbative regime of gauge theories. I describe its application to the study of soft scattering amplitudes in a confining gauge theory. I describe two qualitatively differ...