Polynomial Form of the Stueckelberg Model *

The Stueckelberg model for massive vector fields is cast into a BRS invariant, polynomial form. Its symmetry algebra simplifies to an abelian gauge symmetry which is sufficient to decouple the negative norm states. The propagators fall off like 1/k2 and the Lagrangean is polynomial but it is not powercounting renormalizable due to derivative couplings. ∗)To appear in the Proceedings of the 30th International Symposium Ahrenshoop on the Theory of Elementary Particles, Nuclear Physics B, Proceedings Supplement, edited by D. Lüst, H.-J. Otto and G. Weigt. Research supported by NSF grant no 9309888 and the Swiss National Science Foundation. The Stueckelberg model describes massive vector particles with gauge interactions. It has repeatedly attracted attention [1] as an alternative to the Higgs model and is particularly interesting as long as the Higgs particle is not confirmed experimentally. The model contains a set Aμ a, φa of real vector and scalar fields (a = 1, . . . ,dim(G)) with a gauge invariant kinetic energy and with the interactions of a nonabelian gauge group G, which we take to be simple. The coupling constant g appears as a normalization 1 g in front of the action. Lkin = − 1 4g2 Fμν F (1) Fμν a = ∂μAν a − ∂νAμ a − fbc Aμ Aν c (2) The mass term for the vector fields is introduced in a gauge invariant way. Lmass = − m2 g2 tr (Aμ − U ∂μU) 2 (3) where U = U(φ) is an abbreviation for the series