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this paper might help.$^1$ It's written pedagogically and hence is easier to read. It goes on to discuss a lot more than just color decomposition too. $^1$ Scattering Amplitudes, Henriette Elvang, Yu-tin Huang.


Gluons carry color in color-anticolor pairs and form an octet and a singlet representation as seen below: As you see the octed is filled with a color and an anticolor. The anti has to be a different color otherwise the gluon would be color neutral, and no strong force would be transferred. Since to be exchangeable as gauge bosons in the strong ...

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