COMPLETE CONTROL OF GAUGE PARAMETER DEPENDENCE IN THE ABELIAN HIGGS-MODEL

We examine the dependence on all gauge parameters in the example of th e Abelian Higgs model by applying a general algebraic method which roo ts in an extension of the usual Slavnov-Taylor identity. This method a utomatically yields all information about the gauge parameter dependen ce of Green functions and therefore especially allows to control the r ange of ''good'' normalization conditions. In this context we show tha t the physical on-shell normalization conditions are in complete agree ment with the restrictions dictated by the enlarged Slavnov-Taylor ide ntity and that the coupling can be fixed in an easily handleable way o n the Ward identity of local gauge invariance. As an application of th e general method we also study the Callan-Symanzik equation and the re normalization group equation of the Abelian Higgs model.