A new characterization of BRS-invariant theories with a simple non-Abelian gauge group

For a deeper understanding of the gauge and BRS symmetry it is important to know how non-abelian gauge theories are embedded in general non-invariant models. In order to make this problem accessible to a mathematical analysis the most general renormalizable model with interacting vector and ghost fields is restricted to be invariant under rigid transformations of a simple Lie group, here specifically SU(N). By means of the reduction of couplings it is shown that the non-abelian BRS theories in linear gauge can be characterized within this class of models by the property to be renormalizable and to depend only on one interaction coupling. Analyzing the stability one finds that the BRS solution is completely unstable, i.e. the symmetry is realized in a non-trivial way. (orig.)