Asymptotic Sum Rule in Perturbation Theory

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Abstract
The sum rule which relates the longitudinal cross section in high-energy electron-proton scattering to the Schwinger term in the commutator of the electromagnetic current with itself is investigated in perturbation theory. Various nonperturbative derivations of the sum rule are first reviewed. Then, in second-order perturbation theory (using the gluon model), the failure of the sum rule is shown to be a consequence of the violation of certain of the assumptions which underlie the nonperturbative derivations.