Abstract
Based on the Riemannian geometric approach to Hamiltonian systems with many degrees of freedom, we study a chaotic nature of the SU(2) Yang-Mills field. Particularly, we study the Lyapunov exponent of the Wu-Yang magnetic-monopole solution of the SU(2) Yang-Mills field equation by use of an analytic formula which is determined by the average Ricci curvature and its fluctuation on the Riemannian manifold. It is shown that the system is chaotic from the positive values of the Lyapunov exponent. Furthermore, we find that the energy dependence of Lyapunov exponents exhibits a crossover phenomenon. By using the linear stability analysis, we point out that this crossover is related to the instability of the monopole solution.
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