(1 + 1)-dimensional models of quark confinement and final states in deep-inelastic scattering

Recently (1 + 1)-dimensional quantum electrodynamics has been considered as a model for quark confinement. We calculate the inclusive spectra and multiplicities for deep-inelastic electroproduction and $e^{+}{e}^{-}$ annihilation, and verify the Drell-Yan threshold relations for this model. These analyses are extended to other soluble (1 + 1)-dimensional models of quark confinement. The first is electrodynamics with an additional massive vector gluon. In this theory one can examine the effect of a high-mass threshold on scaling. The theory has a precocious intermediate scaling region below the new threshold in addition to a true canonical asymptotic scaling region. The second model is the quantum electrodynamics of the Thirring model. This is a renormalizable theory which is scale-invariant at short distances. In it one can examine the effect that varying the strength of the short-distance singularity has on inclusive spectra and multiplicities.