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I understand that because the rep. of quark is 3 and antiquark is ##\bar{3}## and we have ##3\otimes \bar{3} = 8\oplus 1##, that a gluon should be 8 or 1, but which one? and why?
Thanks!
Thanks!
This is not really what colour confinement says. By definition of an SU(3) gauge theory, it has 8 generators that transform according to the adjoint representation. This does not include a color singlet, if you added the identity you would get U(3) and not SU(3) so SU(3) does not include a colourless gluon. However, when considering how other fields transform, for example the product ##3 \otimes \bar 3##, the resulting representation needs to be decomposed into irreps and of course such decompositions can contain the trivial representation (in the example ##3\otimes \bar 3 = 8 \otimes 1##).The group representation of SU(3)SU(3)SU(3) mathematically includes this ninth colorless state but gluons can't be colorless on their own which is why (Theory of Color Confinement) we've never seen a lone gluon.