INCREASING POTENTIALS IN CLASSICAL NON-ABELIAN AND ABELIAN GAUGE-THEORIES

An exact solution for an SU(2) Yang-Mills field coupled to a scalar he ld is given, which has potentials with linear, 1/r and 1/r(2) parts. T his may be of some interest since some phenomenological QCD studies as sume a linear plus Coulomb potential. We also show that in the Nielsen -Olesen Abelian model there is an exact solution in the BPS limit, whi ch has a 1/r electromagnetic field and a logarithmically rising scalar field. Both of these solutions must be cutoff from above to avoid inf inite held energy.