# From $U(3)$ to $SU(3)\times U(1)$ Color symmetry. There is a "gluon" photon-like?

Suppose that $U(3)$ was the gauge group. We can decompose this as $U(3)=U(1)\times SU(3)$, which implies that in addition to the $SU(3)$ that has eight generators corresponding to eight gluons, there would be an additional generator for $U(1)$.

Would that generator behave like a photon? (no self interaction and no color)

• Probably yes, but there is an adendum, the coupling would be the strong coupling, and thus, it would couple to electric neutral particles Jun 13, 2014 at 21:31
• It would behave indeed very much like a photon, being the $U(1)$ abelian. Jun 13, 2014 at 21:35
• Related Phys.SE question by OP: physics.stackexchange.com/q/119190/2451 Jun 13, 2014 at 21:36
• @user23873 the coupling could be small and different than those of the gluons. Moreover, even allowing them to be the same at some scale, the running is totally different: one becomes bigger towards the IR whereas feh other becomes smaller in the IR Jun 13, 2014 at 21:37