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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 where
is the current density of the electron where the repeated indices
are summed. However, in Yang-Mills theory the Yang-Mills color
current density of the quark satisfies the equation
which is not a continuity equation () 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 () component of a corresponding
current density by integrating over the entire (physically) allowed volume, the
color charge 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 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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