Renormalizable Lagrangians for massive Yang-Mills fields

Abstract

Renormalizable models are constructed in which local gauge invariance is broken spontaneously. Feynman rules and Ward identities can be found by means of a path integral method, and they can be checked by algebra. In one of these models, which is studied in more detail, local SU(2) is broken in such a way that local U(1) remains as a symmetry. A renormalizable and unitary theory results, with photons, charged massive vector particles, and additional neutral scalar particles. It has three independent parameters. Another model has local SU(2)⊗U(1) as a symmetry and may serve as a renormalizable theory for ϱ-mesons and photons. In such models electromagnetic mass-differences are finite and can be calculated in perturbation theory.