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It is known that every irreducible unitary representation of positive energyof the Poincar\'e group can be realized as a subspace of tensor fields onMinkowski spacetime subjected to suitable partial differential equations. Wefirst describe geometrically the general mechanism that produces, via Fouriertransform, the invariant differential operators corresponding to thoserepresentations. Then, using a super-version of the Fourier transform, we showexplicitly how a massive irreducible unitary representation of the superPoincar\'e group in dimension $(4|4)$ can be realized as a linearsub-supermanifold of suitably constrained superfunctions. In this way, weobtain supersymmetric equations in terms of ordinary (non-Grassmannian) fields.Finally, using the functor of points, we show how our equations can be relatedin a natural way to the Wess-Zumino equations for massive chiral superfields.

Supersymmetric field equations from momentum space