The distinctions between $\mathrm{U}(1)$ and $\mathrm{SU}(3)$ massless bosons

The force carrier particles that mediate the electromagnetic, weak, and strong interactions are called gauge bosons. It is known that the gauge bosons in EM force and strong force are both massless.

A naive question is: why the force behaviors are so distinct from each other? That is --- there is confinement in strong interaction but not electromagnetism?

Can this question be explained without introducing the idea of renormalization group?

The main difference is that the gluon (the force carrier of the strong interaction) is color charged. The photon has no electric charge. Due to the fact that gluons have color charge, they can self-interact, leading to the antiscreening effect.

U(1) is commutative, SU(3) isn't. In a gauge theory, the non-zero commutator implies the appearance of non-linear terms in the field equations, in other words: field-field coupling (you can also say that you get higher-than-second-order terms in the Lagrangian, which is the same way of saying that). A linear field equation, and a non-linear field equation have obviously totally different behaviours.

• I think I actually said the same thing as Andrei, but from a mathematical perspective... Dec 11 '17 at 13:15
• The link in Yang-Mills being that the nonlinear term's coefficient in $D_\mu A_\nu$ is proportional to the gauge boson's self-interacting charge.
– J.G.
Dec 11 '17 at 16:26