The gauge fields in Yang Mills theory are matrices:(adsbygoogle = window.adsbygoogle || []).push({});

A[itex]_{\mu}[/itex] = A[itex]^{a}_{\mu}[/itex] T[itex]^{a}[/itex]

But A[itex]^{a}_{\mu}[/itex] 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!

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# The gauge fields in Yang Mills theory are

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