  Using the functor of points, we prove that the Wess-Zumino equations for
massive chiral superfields in dimension 4|4 can be represented by
supersymmetric equations in terms of superfunctions in the
Berezin-Kostant-Leites sense (involving ordinary fields, with real and complex
valued components). Then, after introducing an appropriate supersymmetric
extension of the Fourier transform, we prove explicitly that these
supersymmetric equations provide a realization of the irreducible unitary
representations with positive mass and zero superspin of the super Poincar\'e
group in dimension 4|4.
