The Gerasimov-Drell-Hearn Sum Rule
  In the confinement regime at Q^2=0 the Gerasimov-Drell-Hearn (GDH) Sum Rule connects static properties of the nucleon with the difference of spin dependent doubly polarized total absorption cross sections of real photons. Now, for the first time this fundamental sum rule is verified by the GDH-Collaboration with circularly polarized real photons and longitudinally polarized nucleons at the two accelerators ELSA and MAMI. The integral (sum) of the GDH Sum Rule can be generalized to the case of virtual photons. This allows to establish a Q^2 dependency and to study the transition to the perturbative regime of QCD. Ultimately, the GDH Sum Rule can be related to the Bjorken and the Ellis-Jaffe Sum Rule. This contribution covers the status of theory concerning the GDH Sum Rule as well as the experimental approaches and their results for the absorption of real and virtual photons. We point out that the so-called No-Subtraction hypothesis, often considered the weakest part of the derivation of the GDH Sum Rule, in fact follows from unitarity and does not impair the fundamental character of the GDH Sum Rule. The shown experimental data verify the GDH Sum Rule for the proton at the level of 8% including the systematic uncertainties from extrapolations to unmeasured energy regions. For the GDH Sum Rule on the neutron and the isovector case we find unexpected contributions at photon energies above 1 GeV. 
Klaus Helbing