these three ingredients appearing systematically in the derivation of all the sum rules which we shall consider. However, in many of the QCD sum rules which we shall later discuss the [*low–energy theorem*]{} will be replaced by a [*high–energy theorem*]{} instead, or rather a [*short–distance behaviour*]{} property which exploits the fact that two–point functions in QCD are known perturbatively at high euclidean momentum transfer due to the asymptotic freedom property of QCD.

The forward Compton–scattering amplitude illustrated by the diagram in Fig. \[fig:Fig1a\],

where $p\cdot q=M_{{\mbox{\scriptsize\rm p}}}\nu$, depends on two scalar invariant amplitudes of the squared energy $\nu^2$: $$A(\nu)=f_{1}(\nu^2)\vec{\epsilon'}\cdot\vec{\epsilon}+
\nu f_{2}(\nu^2)i\vec{\sigma}\cdot\vec{\epsilon'}\times\vec{\epsilon}.$$ The spin–flip amplitude obeys a dispersion relation which is expected to have no subtractions i.e., $${\mbox{\rm Re}}f_{2}(\nu^2)={\mbox{\rm
PP}}\!\int_{0}^{\infty}\frac{d\tilde{\nu}^{2}}{\tilde{\nu}^{2}-\nu^2}
\,\frac{1}{\pi}{\mbox{\rm Im}}f_{2}(\tilde{\nu}^{2}).$$ \[Section \[sec:disperrels\] will be dedicated to the study of dispersion relations in general. They are the basics of sum rule derivations.\] The [*optical theorem*]{} relates ${\mbox{\rm Im}}f_{2}(\nu^2)$ to total cross–sections: $$8\pi\,{\mbox{\rm Im}}f_{2}(\nu^2)=\sigma_{\gamma{\mbox{\rm
p}}}^{\uparrow\downarrow} (\nu)-\sigma_{\gamma{\mbox{\rm
p}}}^{\uparrow\uparrow}(\nu),$$ and the [*low energy–theorem*]{} relates ${\mbox{\rm Re}}f_{2}(0)$ to the proton anomalous magnetic moment squared: $$f_{2}(0)=-\frac{1}{2}\frac{\alpha}{M_{{\mbox{\scriptsize\rm
p}}}^2}\left[F_{2}(0)\right]^2.$$

The [*optical theorem*]{} is a general property of unitarity in quantum field theory. The [*low–energy theorem*]{} follows from chiral symmetry properties of the underlying QCD Lagrangian \[[See the 