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### 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 $\partial_\mu j^\mu(x)=0$ where
$j^\mu(x)$ is the current density of the electron where the repeated indices
$\mu=0,1,2,3$ are summed. However, in Yang-Mills theory the Yang-Mills color
current density $j^{\mu a}(x)$ of the quark satisfies the equation
$D_\mu[A]j^{\mu a}(x)=0$ which is not a continuity equation ($\partial_\mu
j^{\mu a}(x)\neq 0$) 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 ($\mu =0$) component of a corresponding
current density by integrating over the entire (physically) allowed volume, the
color charge $q^a(t)$ 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 $q^a(t)$ 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

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