Compton Scattering on the Proton
  A microscopic coupled-channels model for Compton and pion scattering off the nucleon is introduced which is applicable at the lowest energies (polarizabilities) as well as at GeV energies. To introduce the model first the conventional K-matrix approach is discussed to extend this in a following chapter to the "Dressed K-Matrix" model. The latter approach restores causality, or analyticity, of the amplitude to a large extent. In particular, crossing symmetry, gauge invariance and unitarity are satisfied. The extent of violation of analyticity (causality) is used as an expansion parameter. 
O. Scholten and S. Kondratyuk