Light cone and short distances

Description

In this article short distance and almost light-like distance behaviour of operator products are discussed. In particular, products of electromagnetic and weak currents are treated and applications made to the region of deep inelastic lepton-hadron scattering. This is motivated by the observed scaling behaviour in the deep inelastic region. We review briefly the kinematics and light cone dominance, and then discuss the structure of operator products at nearly light like distances. Light cone expansions are postulated and bilocal operators are introduced. These are a generalization of Wilson's short distance expansion and were abstracted from studies in model field theories. Applications include, among others, treatment of Regge behaviour in relation to sum rules and fixed poles implied by scaling. Regarding models, we discuss the Thirring model and its generalization to include U(n) symmetry. The latter shows scale invariance only for one value of the coupling constant. In both cases anomalous dimensions occur. Regarding field theories in four dimensions, gauge theories are "nearest" to canonical scaling, for which only logarithmic violations occur. We review the quark algebra on the light cone and discuss the applications to structure functions and sum rules. In e+e" annihilation into hadrons we review the various quark schemes. In single particle inclusive annihilation the singularity structure and multiplicity are analyzed. Finally, we comment on various other problems and approaches.