The g1 problem: Deep inelastic electron scattering and the spin of the proton

A recent measurement of the spin-dependent structure function of the proton, g₁^p( x, Q²), suggest that the quark's spin accounts for little of the proton's spin. We analyze several theoretical issues bearing on this result. We discuss the result expected in a variety of quark models. We examine the proposal that gluons contribute to the proton's spin in an amount calculable (in terms of gluon distribution functions) in perturbative QCD. We examine the conserved currents associated with Lorentz transformations in QCD, derive sum rules and show that the anomalous (gluonic) U(1) _A current, K_μ, is not in general to be identified with the gluon spin. Finally, we discuss the ensemble of nucleon matrix elements of quark bilinear operators and urge an experimental and theoretical program to study them.