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 $\nu W_2$ entering the cross section for inelastic electron scattering. These equations relate the $q^2$, $\nu$, and coupling-constant dependence of $W_1$ and $\nu W_2$ 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 $\nu W_2$ in a theory of fermions coupled to pseudoscalar particles and a theory of fermions coupled to vector particles.

• Received 29 June 1972

DOI:https://doi.org/10.1103/PhysRevD.6.3543