  The mechanism of dynamical chiral symmetry breaking is studied in the Abelian
version of the gauged Nambu-Jona-Lasinio model in four dimensions. The most
interesting feature of the gauged Nambu-Jona-Lasinio model is the appearance of
relevant (renormalizable) four-fermion interactions near a critical curve
separating a chiral symmetric and a dynamically chiral symmetry broken phase.
The first three chapters of the thesis are introductory. Chapter 4 is based on
hep-th/9712123. In an attempt to go beyond standard mean field approximations
for four-fermion interactions, the 1/N expansion is utilized in chapter 5.
Within the 1/N expansion, where N is the number of fermion flavors, it is shown
that the renormalization group beta function of the U(1) gauge coupling has
ultra-violet stable fixed points for sufficiently large N. This implies that
the gauged Nambu-Jona-Lasinio model is a rare example of a nontrivial
nonasymptotically free gauge field theory in four dimensions.
