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Yang Mill's Theory of Quantum Chromodynamics
It's not true that quarks can be red, green, or blue. What the truth is that quarks are a vector in a three dimensional color space. If you have two quarks or two different positions, how do you compare them? Well, you need a connection field in between that tells you how to compare them. That connection gives rise to a force field, which in the case of quantum chromodynamics is the gluon.