Renormalization and symmetry conditions in supersymmetric QED

For supersymmetric gauge theories a consistent regularization scheme that p reserves supersymmetry and gauge invariance is not known. In this article w e tackle this problem for supersymmetric QED within the framework of algebr aic renormalization. For practical calculations, a non-invariant regulariza tion scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov-Taylor identity, expressing g auge invariance, supersymmetry and translational invariance, simple symmetr y conditions are derived that are important in a twofold respect: they esta blish exact relations between physical quantities that are valid to all ord ers, and they provide a powerful tool fur the practical determination of th e counterterms. We perform concrete one-loop calculations in dimensional re gularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read of f easily. In addition; a specific example is given how the supersymmetry tr ansformations in one-loop order are modified by non-local terms.