The gauge fields in Yang Mills theory are

by Lapidus
Tags: fields, gauge, mills, theory, yang
 P: 283 The gauge fields in Yang Mills theory are matrices: A$_{\mu}$ = A$^{a}_{\mu}$ T$^{a}$ But A$^{a}_{\mu}$ are vector fields, i.e. a=1,..,n four-vectors. Should not there be a U(1) gauge symmetry for each of them in addition to the non-abelian gauge symmetry? In Lagrangian for the strong force, does not each of these four vectors correspond to a gluon? Gluons or weak bosons are spin-1 particles, so they most be described by four vectors. How do they follow from matrices?? And how can a vector field/ a four-vector be non-abelian?? help, please!
 P: 343 In 4-dimensions each 4-vector corresponds to a spin-one particle(not 4 spin one particles). In SU(N) there are N^2-1 generators so a,b goes from 1 to N^2 -1(not N). In SU(3) that makes 3^2 -1 = 8 gluons $A^a_\mu$