General Theory of Dispersion Sum Rules with Special Emphasis on the High-Energy Contribution

Abstract

A covariant technique to extract the useful sum rules contained in the current commutation relations at equal times has been developed by Fubini. This technique is used to derive the independent sum rules at finite momentum transfer from the $\mathrm{SU}(3)$ current algebra. In particular, we derive the sum rules coming from the commutator of a vector current with its time component where the particles on the outside of the commutator have spin \textonehalf{}. The high-energy contribution to the sum rules is discussed in terms of the Regge poles of the crossed channel. The Regge representation relevant to the kinematics of the amplitude discussed in this paper is treated in detail. The contributions of terms in the commutator other than the usual canonical result are shown to be related to dispersion sum rules more singular at high energy than the usual sum rules. Such contributions are the so-called Schwinger terms.