Asymptotic Sum Rules at Infinite Momentum

By combining the q₀ method for asymptotic sum rules with the P method of Fubini and Furlan, we relate the structure functions W₂ and W₁ in inelastic lepton-nucleon scattering to matrix elements of commutators of currents at almost equal times at infinite momentum. We argue that the infinite-momentum limit for these commutators does not diverge, but may vanish. If the limit is nonvanishing, we predict W₂ (, q^2) f₂ ({q^2}) and W₁ (, q^2) f₁ ({q^2}) as and q^2 tend to. From a similar analysis for neutrino processes, we conclude that at high energies the total neutrino-nucleon cross sections rise linearly with neutrino laboratory energy until nonlocality of the weak current-current coupling sets in. The sum of and \~{}p cross sections is determined by the equal-time commutator of the Cabibbo current with its time derivative, taken between proton states at infinite momentum.