mjhjmtu

It is my understanding that by enforcing SU(3) gauge invariance on our lagrangian of 3-colored quark fields, we are forced to accept the existence of 8 new massless vector fields, the gluons. The 8 here comes directly from the dimension of SU(3).

That being said I often see discussions about the gluons in terms of linear combinations of $rbar r$, $bbar b$, etc.

This simply cant be the nature of the gluons though can it? Because it seems to imply that the number of colors and the number of gluon fuelds are not independant, while they clearly are.

Certainly gluons are not singlets in color space and so they must have color, but it doesnt make sense to me that this color of the gluons would be some mapping directly from quark color.

Thanks to anyone with the insight and time to share it!

The quarks transform according to the fundamental representation $mathbf3$ of SU(3), and the antiquarks according to the conjugate representation $mathbfoverline 3$. The gluons transform according to the adjoint representation $mathbf8$.

The adjoint representation is contained in the product of the fundamental representation and its conjugate:

$$mathbf3otimes mathbfoverline 3 = mathbf8oplus mathbf1$$

Therefore gluons are conventionally labeled using color-anticolor combinations, avoiding the color singlet combination $(roverliner+boverlineb+goverlineg)sqrt3$.

The gluons are generators of the SU(3) gauge group; whatever notation is used to describe the fundamental representation can be extended to higher representations through their embedding in tensor products of the fundamental (and its dual.) [Also, by "sums" of $rbar r$, $bbar b$, etc., do you really mean products?]