Light-Cone Behavior of Perturbation Theory

Abstract

A technique introduced by Symanzik is used to derive a series of equations obeyed order by order in perturbation theory by the structure functions ${W}_{1}$ and $\ensuremath{\nu}{W}_{2}$ entering the cross section for inelastic electron scattering. These equations relate the ${q}^{2}$, $\ensuremath{\nu}$, and coupling-constant dependence of ${W}_{1}$ and $\ensuremath{\nu}{W}_{2}$ in a manner reminiscent of the renormalization-group results of Gell-Mann and Low. The equations are used to compute the leading logarithmic contribution to $\ensuremath{\nu}{W}_{2}$ in a theory of fermions coupled to pseudoscalar particles and a theory of fermions coupled to vector particles.