CLASSICAL GAUGE-THEORIES AS DYNAMICAL-SYSTEMS - REGULARITY AND CHAOS

In this review we present the salient features of dynamical chaos in c lassical gauge theories with spatially homogeneous fields. The chaotic behaviour displayed by both abelian and non-abelian gauge theories an d the effect of the Higgs term in both cases are discussed. The role o f the Chern-Simons term in these theories is examined in detail. Where as, in the abelian case, the pure Chern-Simons-Higgs system is integra ble, addition of the Maxwell term renders the system chaotic. Ln contr ast, the non-abelian Chem-Simons-Higgs system is chaotic both in the p resence and the absence of the Yang-Mills term. We support our conclus ions with numerical studies on plots of phase trajectories and Lyapuno v exponents. Analytical tests of integrability such as the Painleve cr iterion are carried out for these theories. The role of the various te rms in the Hamiltonians for the abelian Higgs, Yang-Mills-Higgs and Ya ng-Mills-Chern-Simons-Higgs systems with spatially homogeneous fields, in determining the nature of order-disorder transitions is highlighte d, and the effects are shown to be counter-intuitive in the last-named system.