Renormalizable massive Yang-Mills theory with intrinsic symmetry breakdown

Abstract

We use the method of the Lagrange multiplier field to construct, within the framework of indefinite-metric field theory, a model of a massive Yang-Mills field, the mass of which derives from an intrinsic symmetry breakdown, rather than a spontaneous symmetry breakdown. The rules for the Feynman diagrams are given. The dynamica structure of the interacting fields is intrinsically related to a local non-Abelian gauge symmetry which renders the theory renormalizable by standard power counting. The part of the amplitude due to the interaction of unphysical particles in the intermediate states, which violates unitarity and gauge symmetry, is isolated and removed, leaving the unitary physical $S$ matrix. The unitarity of the resulting theory, together with its independence with respect to the parameter $\ensuremath{\xi}$, is demonstrated in calculations at the one-loop and the two-loop levels.