Asymptotically Free Yang-Mills Classical Mechanics with Self-Linked Orbits

We construct a classical mechanics Hamiltonian which exhibits spontaneous symmetry breaking akin the Coleman-Weinberg mechanism, dimensional transmutation, and asymptotically free self-similarity congruent with the beta-function of four dimensional Yang-Mills theory. Its classical equations of motion support stable periodic orbits and in a three dimensional projection these orbits are self-linked into topologically nontrivial, toroidal knots. The non-perturbative structure of four dimensional Yang-Mills theory continues to be the subject of extensive investigations. A major goal is the understanding of large distance properties such as color confinement, mass gap and the glueball spectrum. The Yang-Mills theory has also a number of well established salient features like ultraviolet asymptotic freedom and the presence of finite action instantons. Here we shall introduce a classical mechanics Hamiltonian which contains many incredients of the four dimensional Yang-Mills field theory, even though it is defined in a four dimensional phase space. These include asymptotically free self-similarity with a coupling constant that flows like the one loop coupling constant of four dimensional Yang-Mills theory, dimensional transmutation, and spontaneous symmetry breaking akin the Coleman-Weinberg mechanism. Furthermore, we find that its Hamilton’s equations support stable periodic [email protected] [email protected] [email protected]