are boson fields the adjoint of the fermionic field they couple to?

a dull boy

Dear Physics Forum,

I read this on a wikipedia site

"Technically, QCD is a gauge theory with SU(3) gauge symmetry. Quarks are introduced as spinor fields in Nf flavors, each in the fundamental representation (triplet, denoted 3) of the color gauge group, SU(3). The gluons are vector fields in the adjoint representation (octets, denoted 8) of color SU(3)."

and I wanted to know if spin 1 boson fields are always the adjoint of the spin 1/2 fermionic field they couple to, and if so, what does this accomplish mathematically?

Thanks, Mark

fzero

The gauge fields are always in the adjoint representation. There's a few reasons for this, but the most basic is that there needs to be a gauge field for every generator of the gauge group. The adjoint representation is the unique representation that has the same dimension as the group itself.

This has nothing to do with the representations of the matter fields. Nature has somehow chosen that quarks are in fundamental representations, but it is possible to write down gauge theories with matter in other representations.

Ilmrak

Note that the statement on wiki is not that gluons are the adjoint of quarks, but that they are in the adjoint representation of color.

Ilm

a dull boy

Thanks very much, I find this forum very helpful -Mark