Bosonization, effective action, and R-operation in a generalized Nambu-Jona-Lasinio model

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.