  Bosonization in a theory with four-fermion interaction of Nambu-Jona-Lasinio
type with additional U(N) symmetry is studied. It is demonstrated that
bosonization is not uniquely determined by the interaction terms due to Fierz
identities. Effective action including both fermions and composite fields is
constructed. R-operation renormalization scheme is developed for the effective
action. A generalization of bosonization transformation called composite fields
formalism is proposed and demonstrated to be applicable to any field theory.
Nambu-Jona-Lasinio model with three-fermion composite fields is studied as an
example. Fierz identities for sixth-order combinations of fermions are derived.
