Constructive algebraic renormalization of the abelian Higgs-Kibble model

TL;DR

This paper introduces an algebraic renormalization algorithm that systematically restores Slavnov-Taylor invariance at all perturbation orders in the abelian Higgs-Kibble model, simplifying counterterm calculations.

Contribution

It presents a novel algebraic renormalization method for gauge theories, explicitly constructing counterterms using zero-momentum Feynman amplitudes, demonstrated on the abelian Higgs-Kibble model.

Findings

Counterterms involving BRS external sources are eliminated except in the fermion sector.

The method simplifies the calculation of counterterms by using Slavnov-Taylor invariants.

The approach ensures invariance restoration at each perturbation order.

Abstract

We propose an algorithm, based on Algebraic Renormalization, that allows the restoration of Slavnov-Taylor invariance at every order of perturbation expansion for an anomaly-free 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 here discussed in the case of the abelian Higgs-Kibble model, where the zero momentum limit can be safely performed. The normalization conditions are imposed by means of the Slavnov-Taylor invariants and are chosen in order to simplify the calculation of the counterterms. In particular within this model all counterterms involving BRS external sources (anti-fields) can be put to zero with the exception of the fermion sector.