Some solutions of the Yang–Mills equations in dimension greater than four

Abstract

The Yang–Mills equations for gauge fields of an arbitrary semisimple Lie group G in Euclidean spaces Rn with dimension n≥4 is considered. For gauge fields Aa we introduce the ansätze which reduce the Yang–Mills equations in Rn to a set of nonlinear differential matrix equations (Rouhani–Ward equations). This permits us to write out the explicit form of cosmological, plane-wave, and other types of solutions.