Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2012-01-12
Physics
High Energy Physics
High Energy Physics - Phenomenology
32 pages latex
Scientific paper
In Maxwell theory the 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. 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. Since the charge density of a point particle can be obtained from the quantum wave function of that particle, one finds that the charge density of a point particle may depend on space-coordinate ${\vec x}$. However, since the charge of a point particle is obtained from the corresponding charge density after integrating over the entire (physically) allowed volume $V=\int d^3{\vec x}$, one finds that the charge of the point particle can not depend on space-coordinate ${\vec x}$. Since the color charge of the quark is not constant and it can not depend on space coordinate ${\vec x}$, one finds that the color charge $q^a(t)$ of the quark in Yang-Mills theory has to be time dependent. In this paper we derive the general form of eight time dependent fundamental color charges $q^a(t)$ of a quark in Yang-Mills theory in SU(3) where $a=1,2,...8$.
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