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So my principal question is the one in the object above. But then I have another question related.

Supposing I have a $bg$ gluon.

How may I write it in the octet basis?

Thank you for your help!!

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  • $\begingroup$ Some of it is clear (to me), some not. I guess by "base" you mean "basis"? It might help to give a link to explain the octet for people who aren't familiar with it. Also what do you mean by "every one of them with charge" and "...with anti-charge"? You know that gluons always carry a pair of color charge and color anti-charge together, right? What is the "classical base matrix"? $\endgroup$
    – David Z
    Jan 11 '16 at 13:00
  • $\begingroup$ Sorry I meant "basis"! I just wanted to know why (stupid question?) there are not quarks like $bb$ or $rr$ but they only do exist with $b\bar b$ and so on.. $\endgroup$
    – Les Adieux
    Jan 11 '16 at 13:17
  • $\begingroup$ On the issue of 8 vs. 9, see also physics.stackexchange.com/q/119190/2451 , physics.stackexchange.com/q/119202/2451 and links therein. $\endgroup$
    – Qmechanic
    Jan 11 '16 at 13:22
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    $\begingroup$ @KimPeekII Did you mean, why there aren't gluons with charges like $bb$ or $rr$? If so, just ask it like that, it'd be a much better question. $\endgroup$
    – David Z
    Jan 11 '16 at 13:30
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Gluons carry color in color-anticolor pairs and form an octet and a singlet representation as seen below:

gluons

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 interaction gluons have to be part of an octet , these are the acceptable combinations of color/anticolor. A bit similar to the fact that a photon has to be a is singlet, carries no charge.

There exist no free quarks or gluons to be able to set up states with higher color "spins" the way one can do with spin and isotopic spin.

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