Automatic derivation of improved symmetry currents in the context of the Wess-Zumino model

In the context of the free Wess-Zumino model, it is shown how a particular choice of parameters in the expansion of the real superfield in terms of component fields automatically ensures that the stress tensor is traceless and the spinor current J(mu) satisfies gamma .J=0. The currents need not be modified in the usual ad hoc way by the addition of contributions which do not arise in the Noether procedure.