Approximate Integrals in Yang–Mills–Higgs System Using Lie Transforms

Abstract

In this article normalization of a Hamiltonian system with reflection symmetry is performed by means of Lie transforms. The periodic solutions are computed by means of inverse transformation and they are compared with numerical results for the efficiency of the applied method. On the other hand approximate integrals are constructed with the same procedure, and the level curves obtained from those integrals are compared with Poincare surface of section (P.S.S.). The Hamiltonian under consideration is a gauge theoretical model resulting from classical SU(2) Yang–Mills–Higgs system which possesses quartic nonlinear term. The stabilizing effect of Higgs field, suppress the chaotic nature of pure Yang–Mills fields so that regular behaviour becomes dominant. Especially for lower energies the regularity of the system is manifested as invariant curves in P.S.S. Not only periodic orbits but also approximate integrals shows good agreement with numerical results, which improve the reliability of the procedure done.