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When imagining color charged objects, I know we can treat color and anti-color much like electromagnetism. What I'm having trouble with is imagining the interaction of similarly coloured objects. Now I know red green and blue are just convenient labels and by definition of gauge symmetry, aren't different from on another in any way physically. But once we have a basis, how should I think about these 3 independant color charges behaving with eachother?

Lastly, are there any good ways to think about the charge of gluons? They have a color charge behaving differently from quarks or anti-quarks (color and anti-color) so is there anyway to think about this object in analogy to other familiar things?

For what it's worth, I have the mathematical background to do the math, but building intuition is much harder.

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    $\begingroup$ You can visualize the action of $\lambda_3$ or $\lambda_8$ on two similarly colored triplet members? $\endgroup$
    – Cosmas Zachos
    Commented Dec 21, 2018 at 20:24
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    $\begingroup$ How do you think of even the PaulI matrices operating on spinors, in physical terms? Personally, I don't even try, as my assumptions are invariably wrong, ( and it hurts my head. ) +1, tho, related: quora.com/… $\endgroup$
    – user214814
    Commented Dec 21, 2018 at 20:48

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The analogy you're looking for doesn't exist.

  1. There can be no classical analogy for the behaviour of the color-charged objects of QCD because classical Yang-Mills theories behave very differently from quantum Yang-Mills theories in the low-energy regime. This is because theories like QCD become strongly coupled at low energies, and the factor appearing in front of the quantum corrections of a Yang-Mills theory is $g_\text{YM}^2\hbar$, so they do not become irrelevant even if we treat $\hbar$ as small. That is, even if you understood how color-charged objects behave in a classical theory, this would be of little use to understand what is going on in QCD.

  2. Why do you want to "think about the charge of gluons"? The only place where gluons conceivably actually exist as free particles is in high-energy particle collisions, where once again the scattering processes are highly quantum and the only "intuition" we can use is drawing Feynman graphs, but which is also fraught with perils. In all ordinary situations confinement is in effect and you'll never see a single free gluon.

  3. If you absolutely insist on a "just-so" story for what a charge like "red-antiblue" means, it is that such a gluon can interact with a red quark to produce a blue antiquark.

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