Classical Yang-Mills fields with conformal invariance: from exact solutions to qualitative analysis

Abstract

The authors consider classical Yang-Mills equations on Minkowski space, with gauge group SO(3), and look for solutions invariant under a four-dimensional subgroup of the conformal group. In that case, the equations do admit non-Abelian solutions, but these cannot be obtained analytically. Instead, they analyse the equations qualitatively (in a restricted case), in effect treating them as a dynamical system, which turns out to be very simple and completely integrable. The behaviour of the solutions is obtained by singular perturbation methods and the result is confirmed by numerical integration of the equations.