  The major obstacle to a supersymmetric theory on the lattice is the failure
of the Leibniz rule. We analyze this issue by using the Wess-Zumino model and a
general Ginsparg-Wilson operator, which is local and free of species doublers.
We point out that the Leibniz rule could be maintained on the lattice if the
generic momentum $k_{\mu}$ carried by any field variable satisfies
$|ak_{\mu}|<\delta$ in the limit $a\to 0$ for arbitrarily small but finite
$\delta$. This condition is expected to be satisfied generally if the theory is
finite perturbatively, provided that discretization does not induce further
symmetry breaking. We thus first render the continuum Wess-Zumino model finite
by applying the higher derivative regularization which preserves supersymmetry.
We then put this theory on the lattice, which preserves supersymmetry except
for a breaking in interaction terms by the failure of the Leibniz rule. By this
way, we define a lattice Wess-Zumino model which maintains the basic properties
such as $U(1)\times U(1)_{R}$ symmetry and holomorphicity. We show that this
model reproduces continuum theory in the limit $a\to 0$ up to any finite order
in perturbation theory; in this sense all the supersymmetry breaking terms
induced by the failure of the Leibniz rule are irrelevant. We then suggest that
this discretization may work to define a low energy effective theory in a
non-perturbative way.
