is the dynamical quantity, for example a structure function characterizing a particle, and
is the static quantity, for example the mass or the charge of that particle.
The validity of a particular sum rule can be sound if its derivation is based on solid assumptions, or on the contrary, some sum rules have been shown experimentally to be incorrect, due to unwarranted assumptions made in their derivation.
Sum rules are usually obtained by combining a dispersion relation with the optical theorem,[1] using the operator product expansion or current algebra.
[2] Quantum field theory sum rules are useful in a variety of ways.
and integrating it offers a practical way to obtain
is a static quantity, the denomination of sum rule has been extended to the case where