Pion Photoproduction and Fixed-tDispersion Relations

We review the dispersion-theoretic models of the isobar approximation which predict single-pion photo-production in the region of the $\Delta \mathrm{}\left(1236\right)\mathrm{}$ resonance. The differences between the various models are explained and their consequences discussed. Considerable efforts are made to look for further improvements of the theory from the confrontation of theory and experiment. Anticipating the development of experimental techniques, we discuss finally an example for a more complete photoproduction experiment. Specifically, we study the usefulness of a ${\pi }^0$-photoproduction experiment with polarized $\gamma$'s and/or polarized target for the region of the $\Delta \mathrm{}\left(1236\right)\mathrm{}$ resonance.