GAUGE PARAMETER DEPENDENCE AND GAUGE-INVARIANCE IN THE ABELIAN HIGGS-MODEL

We analyze gauge parameter dependence by using an algebraic method whi ch relates the gauge parameter dependence of Green functions to an enl arged Slavnov-Taylor identity. In the course of the renormalization it turns out that gauge parameter dependence of physical parameters is a lready restricted at the level of Green functions. In a first step we consider the on-shell conditions which we find to be in complete agree ment with these restrictions to all orders of perturbation theory. The fixing of the coupling, however, is much more involved outside the co mplete 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 theo ry.