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But what about non-abelian gauge theories? What about N massless spin-1 particles that transfom under SU(N), how do I count their degrees of freedom?

Gluons, for example, are massless spin-1 particles, so I assume that each of them has only two physical dof and the unphysical dof (the longitudal and time-like) can be 'gauged away'. But there are three color gluons that transform in the adjoint rep of SU(N), so that might be too naive, since all three gluons get mixed into each other. But how many physical dof do gluons have?

thank you!