Stability and bifurcation in Yang-Mills theory

Abstract

Whenever gyroscopic forces are present, stable static solutions to dynamical equations of motion need not minimize the energy. We show that this happens in the classical Yang-Mills theory with sources, and we identify the stable fluctuations which lower the energy. The finite form of these infinitesmal, time-dependent deformations of the known static solutions is obtained for weak external sources, and a unified description of both the static and time-varying solutions is given. Also, we demonstrate that the previously found bifurcation in the presence of strong sources is characterized by a zero-eigenvalue mode which dominates the behavior of the solutions near the bifurcation point. The stability properties of the bifurcating solutions are assessed.