Aspects of quark confinement

Various aspects of quark confinement are considered. First, we show in the context of potential theory that steep confinement potentials lead to mass formulas which are similar to those obtained for confining boundary constraints imposed on the free quark motion. We then consider the field-theoretic model of a scalar quark field which is subjected to a strong self-coupling in a finite domain of a three-dimensional lattice space. We show that the strong self- coupling prevents the quark field from spreading easily, but that by itself it does not suffice to confine quarks. A confinement constraint or equivalent potential is still required. We also show that the mass of a single quark grows with increasing self-coupling and becomes infinite in the continuum limit (thus necessitating the use of the lattice). (AIP)