General Form of Color Charge of the Quark

Abstract

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 (${\partial }_{\mu }{j}^{\mu a}(x)\ne 0$) 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.

Comments: 52 pages latex, final version, accepted for publication in Eur. Phys. J. C. arXiv admin note: substantial text overlap with arXiv:1201.2666