Spin one matter fields

Abstract

It is shown how spin one vector matter fields can be coupled to a Yang–Mills theory. Such matter fields are defined as belonging to a representation R of this Yang–Mills gauge algebra \(\mathfrak {g}\). It is also required that these fields together with the original gauge fields be the gauge fields of an embedding total gauge algebra \(\mathfrak {g}_{\textrm{tot}}\). The existence of a physically consistent Yang–Mills action for the total algebra is finally required. These conditions are rather restrictive, as shown in some examples: non-trivial solutions may or may not exist depending on the choice of the original algebra \(\mathfrak {g}\) and of the representation R. Some examples are shown, the case of the initial algebra \(\mathfrak {g}\) = \(\mathfrak {u}(1)\oplus \mathfrak {su}(2)\) being treated in more detail.