  The usual derivation of the Lagrangian of a model for massive vector bosons,
by spontaneous symmetry breaking of a gauge theory, implies that the prefactors
of the various interaction terms are uniquely determined functions of the
coupling constant(s) and the masses. Since, under the renormalization group
(RG) flow, different interaction terms get different loop-corrections, it is
uncertain, whether these functions remain fixed under this flow. We investigate
this question for the $U(1)$-Higgs-model to 1-loop order in the framework of
Epstein-Glaser renormalization. Our main result reads: choosing the
renormalization mass scale(s) in a way corresponding to the minimal subtraction
scheme, the geometrical interpretation as a spontaneously broken gauge theory
gets lost under the RG-flow. This holds also for the clearly stronger property
of BRST-invariance of the Lagrangian. On the other hand we prove that physical
consistency, which is a weak form of BRST-invariance of the time-ordered
products, is maintained under the RG-flow.
