Eur. Phys. J. C (2013) 73: 2442
https://doi.org/10.1140/epjc/s10052-013-2442-6

Regular Article - Theoretical Physics

General form of color charge of the quark

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^* e-mail: nayak@max2.physics.sunysb.edu

Received: 13 April 2012
Revised: 31 March 2013
Published online: 5 June 2013

Abstract

In Maxwell theory the constant electric charge e of the electron is consistent with the continuity equation ∂ _μ j ^μ (x)=0 where j ^μ (x) is the current density of the electron where the repeated indices μ=0,1,2,3 are summed. However, in Yang–Mills theory the Yang–Mills color current density j ^μa (x) of the quark satisfies the equation D _μ [A]j ^μa (x)=0 which is not a continuity equation (∂ _μ j ^μa (x)≠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) 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.