Determination of Yang-Mills potentials from the field strengths

The existence and uniqueness of a Yang-Mills potential for a given field strength is discussed. Previous results are reviewed. In two space-time dimensions every nonzero field strength can be derived from any element of a very large class of potentials which are not related by a gauge transformation. We exhibit these potentials explicitly. In four dimensions we show that both a constant electric field and a Coulomb field can be described by a variety of nongauge-related potentials which describe very different physical situations