Wess-Zumino Model in the Causal Approach

TL;DR

This paper demonstrates that the Wess-Zumino model maintains supersymmetry invariance at all perturbation orders within the causal Epstein-Glaser approach, confirming the absence of anomalies through algebraic methods without Grassmann variables.

Contribution

It proves supersymmetry invariance can be preserved at all orders in the causal approach, showing anomalies are absent algebraically without Grassmann variables.

Findings

Supersymmetry invariance holds at all perturbation orders.

Anomalies are proven to be absent in the model.

The approach avoids Grassmann variables, simplifying the framework.

Abstract

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 the gauge invariance in the Z\"urich 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 purely algebraic nature. We work consistently in the quantum framework based on Bogoliubov axioms of perturbation theory so no Grassmann variables are necessary.