Spin One Matter Fields

TL;DR

This paper explores how spin one vector matter fields can be integrated into Yang-Mills theories by embedding them into a larger gauge algebra, with the existence of consistent actions depending on algebraic choices.

Contribution

It provides a framework for coupling spin one matter fields to Yang-Mills theories via algebra embeddings and analyzes the conditions for consistent gauge actions.

Findings

Existence of solutions depends on algebra and representation choices.

Examples demonstrate when consistent couplings are possible.

Detailed analysis of the case with algebra $$ and $$.

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 $\mathfrak{g}_{\rm tot}$. 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.