  Based on the Cornwall-Jackiw-Tomboulis effective potential, we extensively
study nonperturbative renormalization of the gauged Nambu-Jona-Lasinio model in
the ladder approximation with standing gauge coupling. Although the pure
Nambu-Jona-Lasinio model is not renormalizable, presence of the gauge
interaction makes it possible that the theory is renormalized as an interacting
continuum theory at the critical line in the ladder approximation. Extra higher
dimensional operators (``counter terms'') are not needed for the theory to be
renormalized. By virtue of the effective potential approach, the
renormalization (``symmetric renormalization'') is performed in a
phase-independent manner both for the symmetric and the spontaneously broken
phases of the chiral symmetry. We explicitly obtain $\beta$ function having a
nontrivial ultraviolet fixed line for the renormalized coupling as well as the
bare one. In both phases the anomalous dimension is very large ($ \ge 1$)
without discontinuity across the fixed line. Operator product expansion is
explicitly constructed, which is consistent with the large anomalous dimension
owing to the appearance of the nontrivial extra power behavior in the Wilson
coefficient for the unit operator. The symmetric renormalization breaks down at
the critical gauge coupling, which is cured by the generalized renormalization
scheme (``$\tM$-dependent renormalization''). Also emphasized is the formal
resemblance to the four-fermion theory in less than four dimensions which is
renormalizable in $1/N$ expansion.
