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    General Form of Color Charge of the Quark

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    In Maxwell theory the constant electric charge e of the electron is consistent with the continuity equation μjμ(x)=0\partial_\mu j^\mu(x)=0 where jμ(x)j^\mu(x) is the current density of the electron where the repeated indices μ=0,1,2,3\mu=0,1,2,3 are summed. However, in Yang-Mills theory the Yang-Mills color current density jμa(x)j^{\mu a}(x) of the quark satisfies the equation Dμ[A]jμa(x)=0D_\mu[A]j^{\mu a}(x)=0 which is not a continuity equation (μjμa(x)0\partial_\mu j^{\mu a}(x)\neq 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\mu =0) component of a corresponding current density by integrating over the entire (physically) allowed volume, the color charge qa(t)q^a(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)q^a(t) of the quark in Yang-Mills theory in SU(3) where a=1,2,...,8.Comment: 52 pages latex, final version, accepted for publication in Eur. Phys. J. C. arXiv admin note: substantial text overlap with arXiv:1201.266