Gauge parameter dependence and gauge invariance in the Abelian Higgs model

TL;DR

This paper investigates how gauge parameter dependence affects Green functions and physical parameters in the Abelian Higgs model, establishing conditions for gauge invariance and proper fixing of parameters through algebraic and Ward identity methods.

Contribution

It introduces an algebraic approach linking gauge parameter dependence to an extended Slavnov-Taylor identity and demonstrates gauge invariance fixing via Ward identities in the Abelian Higgs model.

Findings

Gauge parameter dependence of physical parameters is restricted at the Green function level.

On-shell conditions align with these restrictions to all orders.

Proper fixing of the coupling is achieved through Ward identities in the Abelian Higgs model.

Abstract

We analyze gauge parameter dependence by using an algebraic method which relates the gauge parameter dependence of Green functions to an enlarged Slavnov-Taylor identity. In the course of the renormalization it turns out that gauge parameter dependence of physical parameters is already restricted at the level of Green functions. In a first step we consider the on-shell conditions which we find to be in complete agreement with these restrictions to all orders of perturbation theory. The fixing of the coupling, however, is much more involved outside the complete on-shell scheme. In the Abelian Higgs model we prove that this fixing can be properly chosen by requiring the Ward identity of gauge invariance to hold in its tree form to all orders of perturbation theory.