  In an effort to investigate some of the low energy properties of QCD, in
particular those related to chiral symmetry breaking, as well as to obtain
insights on the behavior of an interacting theory of fermions on the lattice,
the two flavor Nambu--Jona-Lasinio model with $SU(2) \times SU(2)$ chiral
symmetry is studied on the four--dimensional hypercubic lattice using large $N$
techniques and numerical simulations. Naive and Wilson fermions are considered
and transparent results are obtained regarding the following: the scalar and
pseudoscalar spectrum, the approach to the continuum and chiral limits, the
size of the $1/N$ corrections, and the effects of the zero momentum fermionic
modes on finite lattices. Also, some interesting observations are made by
viewing the model as an embedding theory of the Higgs sector. Note: The full ps
file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu.
To get the ps file, ftp to this address and use for username "anonymous" and
for password your name. The file is in the directory pub/vranas (to go to that
directory type: cd pub/vranas) and is called NJL.ps (to get it type: get
NJL.ps)
