Class of complex Yang-Mills fields

Abstract

We give a procedure by means of which a class of solutions of the SU(2) Yang-Mills equations in Minkowski space-time is obtained. The potentials and field strengths generated by our method are complex. However, the corresponding energy-momentum tensor is a real quantity. We obtain a subset of SU(2) solutions starting from solutions of the wave equation. These SU(2) solutions have vanishing energy-momentum tensors, even though they are not obtained by a gauge transformation from the vacuum. We exhibit also a simple nonsingular time-dependent SU(2) solution and discuss a Liénard-Wiechert type of solution in SU(2). © 1978 The American Physical Society.