Chaotic Versus Regular Behavior in Yang-Mills Theories

Abstract

We consider spatially uniform $SU(2)$ color fields. At the classical level the system exhibits almost exclusively chaotic behavior. To include quantum effects, we introduce a renormalization-group improved effective action, where the fixed coupling constant $g$ is replaced by a running coupling constant $g$, depending upon the color magnetic field. The effective Lagrangian gives rise to invariant tori which occupy a significant portion of the phase space and sustain ordered behavior. For some energy values, stable periodic orbits exist, with the corresponding gluon field being color neutral.