Wess-Zumino model in the causal approach

The Wess–Zumino model is analysed in the framework of the causal approach of Epstein–Glaser. The condition of invariance with respect to supersymmetry transformations is similar to gauge invariance in the Zürich formulation. We prove that this invariance condition can be implemented in all orders of perturbation theory, i.e. the anomalies are absent in all orders. This result is of a purely algebraic nature. We work consistently in the quantum framework based on the Bogoliubov axioms of perturbation theory, so no Grassmann variables are necessary.