Topologically-Stable Protons and Neutrons, and how to Analytically Path Integrate the Yang-Mills Action

Abstract: We develop in detail, the classical magnetic monopoles of non-abelian Yang-Mills gauge theory and show how these monopoles, when analyzed using Gauss ’ / Stokes ’ theorem, appear to confine their gauge fields, and also, appear to be composite objects. Of course, baryons, which include the protons and neutrons at the heart of nuclear physics, also confine their gauge fields and are similarly-composite objects. This raises the question whether the magnetic monopoles of Yang-Mills theory are in some fashion related to the observed physical baryons. After developing inverse solutions for the non-abelian electric charge densities while carefully examining uniqueness and gauge fixing, we use these solutions together with Dirac theory to “populate ” these classical monopoles with fermions. Applying the Fermi-Dirac-Pauli Exclusion Principle to these fermions forces the selection of a dimension-3 gauge group initially chosen to be SU(3). We then find that these non-abelian magnetic monopoles have the exact chromodynamic symmetries of baryons and interact via colored magnetic fields with the exact chromodynamic symmetries of mesons. We show that a required U(1) factor ensures that these monopoles are topologically stable, and also “flavors ” these monopole as protons and neutrons. Because this exposition is classical, we also discuss the extent to which classical fiel