General form of color charge of the quark

In Maxwell theory the constant electric charge e of the electron is consistent with the continuity equation ∂μ jμ (x)=0 where jμ (x) is the current density of the electron where the repeated indices μ=0,1,2,3 are summed. However, in Yang-Mills theory the Yang-Mills color current density jμa(x) of the quark satisfies the equation Dμ [A]jμa(x)=0 which is not a continuity equation (∂μ jμa(x) ≠0) which implies that the color charge of the quark is not constant where a=1,2..,8 are the color indices. Since the charge of a point particle is obtained from the zero (μ=0) component of a corresponding current density by integrating over the entire (physically) allowed volume, the color charge qa(t) of the quark in Yang-Mills theory is time dependent. In this paper we derive the general form of eight time dependent fundamental color charges qa(t) of the quark in Yang-Mills theory in SU(3) where a=1,2..,8. (orig.)