Some classical properties of the non-abelian Yang-Mills theories

Abstract

We present some classical properties for non-abelian Yang-Mills theories that we extract directly from the Maxwell's equations of the theory. We write the equations of motion for the $SU(3)$ Yang-Mills theory using the language of Maxwell's equations in both differential and integral forms. We show that vectorial gauge fields in this theory are non-fermionic sources for non-abelian electric and magnetic fields. These vectorial gauge fields are also responsible for the existence of magnetic monopoles. We build the continuity equation and the energy-momentum tensor for the non-abelian case.