Hi,
Quote by abbottsys
Thanks, but I was hoping to get a simple explanation without diving into SU(3) mathematics. For example: each charge has 2 values, and number of charges in the color field =3, so then we have 2^3 = 8. Can this be justified by gauge theory? And does the same formula work for other gauge fields, such as the electroweak field?

The answer is no for both questions.
3 Charges: because the quarks are in the triplet representation of SU(3)
8 Gluons : because the gauge bosons are in the adjoint representation, that has dimension 8.
These two numbers (3 and 8) are not
a priori related to each other, as you can put your matter fields in any representation (not only triplet) (but you don't actually do it for physical reasons).