Why Are There Only 8 Gluons in Quantum Chromodynamics?

[Allojubrious]

8 Gluons...?

I am studying quarks again, and the gluons that are exchanged, and I really want to learn about WHY ARE THERE ONLY 8 GLUONS? This has been puzzling me so I was wondering if somebody could help me!

Thanks.

 

[chrispb]

The adjoint of SU(3), the gauge group corresponding to color, is 8 (=3^2-1)-dimensional. The gluon field (or any connection, for that matter) transforms as the adjoint of the gauge group. Therefore, there are 8 independent types of gluons that one could imagine exchanging.

 

[Bill_K]

The ninth gluon, if it existed, would be a color singlet. As a colorless particle it would not participate in the nonlinear color interaction that causes confinement of the other gluons and the quarks. It would therefore be a free massless particle with long-range interaction. Such a particle would easily be observed, and has not been.

 

[tom.stoer]

One can understand this mathematically quite easily. You know the SU(3) generators, the so-called Gell-Mann lambda matrices. Now going from SU(3) to U(3) is the same as to U(1)*SU(3); so the additional generator is the generator of the U(1) factor. But this is nothing else but the identity matrix, i.e. 1. Of course 1 commutes with all other generators which is what Bill_K means when he is talking about a color singulet.

 

[Allojubrious]

Thank you for the help!

 

[Finbar]

Question: If I had a gauge theory U(3) is this equivalent to U(1)xSU(3)? In which case it would be QCD coupled to QED in the "9th gluon" would be the photon i.e. "a free massless particle with long-range interaction" ??

 

[tom.stoer]

U(3) = U(1) * SU(3) is correct