Eikonal approximation for deep inelastic scattering in scalar electrodynamics

Functional integration in the eikonal approximation is used to study the cross section of deep inelastic scattering in scalar electrodynamics. An explicit expression is obtained for the structure functions in the Björken limit; scaling of $\nu W_2$ is violated by a logarithmic dependence on the asymptotic variable $\nu$. At large $\nu$, $\nu W_2$ in this approximation decreases as the square of the elastic form factor, and $W_1$ vanishes to the accuracy adopted in the calculations.