SU(3) Maxwell equations and the classical chromodynamics
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We study the equations of motion of the SU(3) Yang-Mills theory. Since the gluons, at scales of the order of 1 $fm$, can be considered as classical fields, we suppose that the gauge fields ($A_μ^a$) of this theory are the gluonic fields and then it is possible to consider the Quantum Chromodynamics in a classical regime. For the case in which the condition $[A_μ^a, A_ρ^a]=0$ is satisfied, we show that the abelian equations of motion of the Classical Chromodynamics (CCD) have the same form as those of the classical electrodynamics without sources. Additionally, we obtain the non-abelian Maxwell equations for the CCD with sources. We observe that there exist electric and magnetic colour fields whose origin is not fermionic. We show as the gluons can be assumed as the sources of the electric and magnetic colour fields. We note that the gluons are the only responsible for the existence of a magnetic colour monopole in the CCD.
9 pages. Some small changes have been performed
9 pages. Some small changes have been performed