  It is known that every irreducible unitary representation of positive energy
of the Poincar\'e group can be realized as a subspace of tensor fields on
Minkowski spacetime subjected to suitable partial differential equations. We
first describe geometrically the general mechanism that produces, via Fourier
transform, the invariant differential operators corresponding to those
representations. Then, using a super-version of the Fourier transform, we show
explicitly how a massive irreducible unitary representation of the super
Poincar\'e group in dimension $(4|4)$ can be realized as a linear
sub-supermanifold of suitably constrained superfunctions. In this way, we
obtain supersymmetric equations in terms of ordinary (non-Grassmannian) fields.
Finally, using the functor of points, we show how our equations can be related
in a natural way to the Wess-Zumino equations for massive chiral superfields.
