**73**: 2442

https://doi.org/10.1140/epjc/s10052-013-2442-6

Regular Article - Theoretical Physics

## General form of color charge of the quark

1001 East 9th Street, #A, Tucson, AZ, 85719, USA

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

Received:
13
April
2012

Revised:
31
March
2013

Published online:
5
June
2013

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.

*© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013*