In this paper we reconcile two contradictory statements about deep inelastic scattering (DIS) in manifestly covariant theories: (i) the scattering must be gauge invariant, even in the deep inelastic limit, and (ii) the pole term (which is not gauge invariant in a covariant theory) dominates the scattering amplitude in the deep inelastic limit. An "intermediate" answer is found to be true. We show that, at all energies, the gauge dependent part of the pole term cancels the gauge dependent part of the rescattering term, so that both the pole and rescattering terms can be separately redefined in a gauge invariant fashion. The resulting, redefined pole term is then shown to dominate the scattering in the deep inelastic limit. Details are worked out for a simple example in 1+1 dimensions.

We studied meson-meson interactions using the 't Hooft model, which represents QCD in 1 + 1 dimensions and assumes a large number of colors ͑N c ͒. The dominant interactions in this large N c limit are generated by quark exchange. Our results show that QCD in 1 + 1 dimensions allows the realization of a constituent-type quark model for the mesons and generates a scalar ""-like meson-meson resonance, whose effective coupling and mass are determined by the underlying QCD dynamics. These results suggest an interpretation of the lightest scalar mesons as qqqq systems.

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We present an elementary nonperturbative method to obtain Green's functions (GFs) for timelike momenta. We assume there are no singularities in the second and the fourth quadrants of the complex plane of space momentum components and perform a 3d analogue of Wick rotation. This procedure defines Greens functions in a timelike Euclidean space. As an example we consider the quark propagator in QCD. While for weak coupling, this method is obviously equivalent to perturbation theory, for a realistic QCD coupling a complex part of the quark mass and renormalization wave function has been spontaneously generated even below the standard perturbative threshold. Therefore, our method favors a confinement mechanism based on the lack of real poles.