Classical models of confinement

We investigate the structure of classical models of confinement by analytic methods. The models considered involve just one abelian gauge field and can be viewed as non-linear versions of Maxwell's theory. We study in detail the case of two opposite static point charges. A scaling law is found for small separations of the charges, while a perturbation treatment is developed for large separations. The results obtained for large separations include an exact evaluation of the first correction term to the linear potential and a classification of the asymptotic field configurations. (orig.)