Dynamical chaos in SU(2)⊗U(1) theory

Abstract

We study the dynamics of the classical homogeneous SU(2)⊗U(1) gauge theory in the spontaneously broken phase. A transition from regular to chaotic dynamics is shown to occur for energy densities ε>0.3 m W 2/ G F≈2×10 10 GeV/fm 3. The regular regime is characterized by a sharp frequency spectrum for the Yang-Mills fields. The frequency spectrum in the chaotic regime is continuous and the sharp frequency lines of the regular regime are dispersed. In the early universe or at high energy densities in a Yang-Mills plasma this transition may have observable effects that can be studied by analyzing the frequency spectrum and the time correlation functions. In the chaotic regime these time correlation functions decay considerably faster than in the regular regime.