A four-dimensional massive gauge model: the spontaneous symmetry breakdown of the second kind

Abstract

A gauge-invariant Abelian field model with massive fermion and massive gauge vector-boson fields is formulated with, the help of a scalar Stueckelberg field. This model does not need any Higgs-like particles, and the scalar field (associated with the longitudinal part of the gauge vector boson) generally is arbitrary. When this scalar field is chosen to be a massive field, the gauge transformations become restrictive. The spontaneous symmetry breakdown, associated with the massive scalar field, is of the « second kind »,i.e. different than the usual spontaneous symmetry breakdown. Also in the presence of the massive scalar field, the quantization of the massive gauge boson field is carried out and then conjectured for arbitrary scalar fields (arbitrary gauges). In this connection, the propagator of the massive gauge boson is also discussed. Furthermore, it is shown that this model can be associated with the corresponding Higgs model if the « massless » Goldstone field is proportional to the arbitrary (and, in special cases, massive) scalar field, and if the Higgs field is set equal to zero. Finally, it is argued that, at least when the scalar field is massive, this model is renormalizable.