  We investigate two-dimensional Wess-Zumino models in the continuum and on
spatial lattices in detail. We show that a non-antisymmetric lattice derivative
not only excludes chiral fermions but in addition introduces supersymmetry
breaking lattice artifacts. We study the nonlocal and antisymmetric SLAC
derivative which allows for chiral fermions without doublers and minimizes
those artifacts. The supercharges of the lattice Wess-Zumino models are
obtained by dimensional reduction of Dirac operators in high-dimensional
spaces. The normalizable zero modes of the models with N=1 and N=2
supersymmetry are counted and constructed in the weak- and strong-coupling
limits. Together with known methods from operator theory this gives us complete
control of the zero mode sector of these theories for arbitrary coupling.
