Dynamics of classical Yang Mills fields coupled to Higgs field

Classical Yang Mills fields are analyzed in the context of nonlinear dynamical systems. Although the theory is described by complicated set of coupled partial differential equations, under specific ansatzes it is possible to obtain simpler dynamical system whose equations of motion can be represented by coupled ordinary differential equations. It is numerically shown that the reduced system possesses chaotic behaviour. On the other hand, the coupling of Higgs field stabilizes chaotic behavior of Yang Mills fields. This stabilization can be attributed to the additional harmonic oscillator part appearing in the Hamiltonian. It is numerically verified that the coefficient of harmonic oscillator term dramatically changes the behavior of the system corresponding to two different Yang-Mills-Higgs systems. For fixed energy, a small increase in the coefficient suppresses the chaos and the system is dominated with quasiperiodic and periodic solutions. Even if the reduced mechanical systems are simpler than the original ones, still it is not possible to express the solutions with elementary functions. But using perturbation theory one can make good prediction for dynamics of the system. For this purpose, Lie Transform perturbation theory is used which is a very efficient tool especially for Hamiltonian systems. With the implemented algorithm approximate integrals are constructed beside the normalized solutions. Those solutions and integrals are expressed as a series, and they are used to simulate the mechanical system. Although the convergence of series is not guaranteed they turn out to be in good agreement with the numerical results, especially for the periodic and quasiperiodic regimes.