Nonlinear stability and small fluctuations around a classical Yang-Mills ground state

It is well known that a classical uniform Yang-Mills magnetic field is unstable under small fluctuations. We study the nonlinear stability of such a system. Assuming that only the unstable modes are important, we develop an approximation method to describe the interaction among these modes. We investigate the true classical ground state of this system and obtain the frequency of small fluctuations around it.