Compton Scattering and Generalized Polarizabilities

In recent years, real and virtual Compton scattering off the nucleon have attracted considerable interest from both the experimental and theoretical sides. Real Compton scattering gives access to the so-called electromagnetic polarizabilities containing the structure information beyond the global properties of the nucleon such as its charge, mass, and magnetic moment. These polarizabilities have an intuitive interpretation in terms of induced dipole moments and thus characterize the response of the constituents of the nucleon to a soft external stimulus. The virtual Compton scattering reaction $e^-p\to e^-p\gamma$ allows one to map out the {\em local} response to external fields and can be described in terms of generalized electromagnetic polarizabilities. A simple classical interpretation in terms of the induced electric and magnetic polarization densities is proposed. We will discuss experimental results for the polarizabilities of the proton and compare them with theoretical predictions.