Recent string theory developments suggest the necessity to understand super
symmetric gauge theories non-perturbatively, in various dimensions. In this
work we show that there is a standard Hamiltonian formulation that generat
es a finite and supersymmetric result at every order of the approximation s
cheme known as discrete light-cone quantization (DLCQ), We present this ren
ormalized DLCQ Hamiltonian and find that it has two novel features: it auto
matically chooses the 't Hooft prescription for renormalizing the singulari
ties, and it introduces irrelevant operators that serve to preserve the sup
ersymmetry and improve the convergence. We solve for the bound states and t
he wave functions with and without the irrelevant operators and verify that
with the irrelevant operator the exact large-N-C supersymmetric DLCQ (SDLC
Q) results are reproduced. With the irrelevant operator removed, we show th
at the hound-state mass and wave functions appear to he converging to the S
DLCQ results but very slowly. This is a first step in extending the advanta
ges of SDLCQ to non-supersymmetric theories. (C) 2001 Published by Elsevier
Science B.V.