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I have already seen this question. It was answered that $U(3)$ can be decomposed into $SU(3) \times U(1)$, and $U(1)$ is already used for the EM interaction. Still, I wonder why the EM interaction influences the strong one. A linear combination of three gluon-antigluon states would be conceivable, as far as I can see. The matrix of gluon antigluon states has trace zero, but why should this depend on the fact that $U(1)$ has been used already for EM?

In other words, is the $U(1)$ transformation used in EM the cause that it's absent in the $SU(3)$ transformation used in the color force? Is this the reason $SU(3)$ was chosen and not $U(3)$, or was it the absence of colorless states of three gluon-antigluon states (would these be able to travel like real photons, like a kind of gluon balls?).

Qmechanic
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MatterGauge
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1 Answers1

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In short, no.

One of the answers to the other question does say that the strong force gauge group can't have an extra factor of $U(1)$ because "total phase rotations of the quark wave function are already part of the model", referring to the $U(1)$ factor in the Standard Model gauge group.

The $U(1)$ factor in that answer isn't electromagnetic $U(1)$, which is a different subgroup of $SU(2)\times U(1)$.

More importantly, though, the answer is just wrong. Identifying a $U(1)$ factor in the gauge group with complex phase is just a convention. You can add additional $U(1)$ forces; they aren't in the Standard Model simply because they aren't observed (as the other, better answer said).

benrg
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