lectures of Pich [@PiclesH] and Manohar [@ManlesH] in this school.]{}\] The [*dispersion relation*]{} for forward scattering amplitudes is also a general property of quantum field theory [@GGT54]. What is still lacking to promote this sum rule to the status of a QCD theorem is the proof that ${\mbox{\rm Im}}f_{2}(\nu^2){\rightarrow}0$ when $\nu{\rightarrow}\infty$. At present this accepted behaviour is only supported by theoretical strong interaction wisdom, like Regge phenomenology.

The Drell–Hearn sum rule has been checked in perturbation theory in QED–like theories to the first non–trivial order. One may ask if this sum rule could be used for practical calculations of the anomalous magnetic moment of the electron. The answer is that it is not a competitive method, simply because $F_{2}(0)$ in the l.h.s. appears squared which obliges one to calculate the integral in the r.h.s. to very high orders in powers of the fine structure constant.

The Drell–Hearn sum rule is also useful in the phenomenological study of deep inelastic scattering of polarized leptons on polarized protons \[[See Manohar’s lectures [@ManlesH] in this school.]{}\], where it provides a constraint on the limit of real photoabsorption. It plays an important rôle as well in the calculation of the so called [*polarizability*]{} contribution 