RIGID INVARIANCE AS DERIVED FROM BRS INVARIANCE - THE ABELIAN HIGGS-MODEL

Consequences of a symmetry, e.g. relations amongst Green functions, ar e renormalization scheme independently expressed in terms of a rigid W ard identity. The corresponding local Version yields information on th e respective current. In the case of spontaneous breakdown one has to define the theory via the BRS invariance and thus to construct rigid a nd current Ward identity non-trivially in accordance with it. We perfo rmed this construction to all orders of perturbation theory in the abe lian Higgs model as a prelude to the standard model. A technical tool of interest in itself is the use of a doublet of external scalar ''bac kground'' fields. The Callan-Symanzik equation has an interesting form and follows easily once the rigid invariance is established.