Inelastic electron-proton scattering and a sum rule for the Schwinger term

Abstract

It is shown that the form of the one-particle expectation value of the Schwinger term in the equal-time commutator of the electromagnetic current and change densities is determined by relativistic covariance. This allows us to derive a sum rule for the one-proton expectation value of the Schwinger term involving the structure function W₂ measured in inelastic electron-proton scattering. From this sum rule for the Schwinger term one can obtain the sum rule d/dq²∫0^∞dννW₂(q², ν)/q²=0, where q² is the square of the four-momentum transfer, and ν is the energy loss of the electron in the laboratory frame. We compare this equation with the recent experimental data using "scale invariance." We find from this comparison that this sum rule is reasonably well satisfied.