Results from a study of the Nambu--Jona-Lasinio model on the lattice

The main results of our analysis of the two flavor Nambu--Jona-Lasinio model with $SU(2) \times SU(2)$ chiral symmetry on the four--dimensional hypercubic lattice with naive and Wilson fermions are presented. Large $N$ techniques and numerical simulations are used to study various properties of the model. 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 are studied. Also, some interesting observations are made by viewing the model as an embedding theory of the Higgs sector.