Origin of external sources for classical Yang-Mills fields.

Abstract

An effort to derive the classical Yang-Mills equation with an external color four-current density ${j}^{a\ensuremath{\mu}}$(x) from a more fundamental theory is presented. It is shown that in the case of an arbitrary static external color charge, i.e., when ${j}^{a\ensuremath{\mu}}$=${\ensuremath{\delta}}_{0}^{\ensuremath{\mu}}$${\ensuremath{\rho}}^{a}$(x), the classical Yang-Mills equation follows from the closed set of classical Yang-Mills and Dirac equations in the limit m\ensuremath{\rightarrow}\ensuremath{\infty}, where m is the mass of the Dirac particle. In the case of the classical Yang-Mills equation with an external color current ${j}^{\mathrm{ai}}$, i=1,2,3, no such derivation is found.