Dynamical symmetry breakdown in pure Yang-Mills field theory

It is shown, in a simple approximation consistent with gauge invariance, that Yang-Mills fields associated with a compact simple Lie group, may acquire mass through their self-interactions; this phenomenon leads to a breakdown of the original group symmetry and to an eigenvalue condition for the coupling constant of the self-interaction. It is conjectured, from an analysis of Feynman graphs, that these facts are still true in the full theory. The relevance of these conclusions to the problem of fermions interacting with Yang-Mills mesons is pointed out.