Constructive algebraic renormalization of the Abelian Higgs-Kibble model

We propose an algorithm, based on algebraic renormalization, that allows the restoration of Slavnov-Taylor invariance at every order of perturbative expansion for an anomaly-free Becchi-Rouet-Stora (BRS) invariant gauge theory. The counterterms are explicitly constructed in terms of a set of one-particle-irreducible Feynman amplitudes evaluated at zero momentum (and derivatives of them). The approach is discussed here in the case of the Abelian Higgs-Kibble model (in $3+1$ dimensions), where the zero momentum limit can be safely performed. The normalization conditions are imposed by means of the Slavnov-Taylor invariants. A judicious choice of the normalization conditions greatly simplifies the calculation of the counterterms. In particular within this model all counterterms involving BRS external sources (antifields) can be put to zero with the exception of the fermion sector.