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

TL;DR

This paper introduces a classical mechanics Hamiltonian model that mimics key features of Yang-Mills theory, including asymptotic freedom and topologically complex orbits, providing insights into nonperturbative phenomena.

Contribution

It constructs a classical Hamiltonian exhibiting symmetry breaking, dimensional transmutation, and self-similarity aligned with Yang-Mills theory, with stable, topologically knotted periodic orbits.

Findings

Supports stable periodic orbits with nontrivial topology

Replicates the beta-function behavior of Yang-Mills theory

Demonstrates classical analogs of quantum phenomena

Abstract

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.