Based on chiral Ward-Takahashi identities with composite fields, we develop a method to investigate fermion mass generation and bound-state spectra in the ( 2 + 1 )-dimensional chiral Gross-Neveu model. PACS number(s): 11.15.Ex, 11.30.RdAlthough it is commonly accepted that QCD is the theory of strong interactions, at nuclear length scales the coupling constant is really strong and does not allow for a systematic perturbative expansion, which means that nonperturbative schemes ought to be taken into account. Because of the inherent difficulties in attempting to study nonperturbative phenomena [I], the bound-state spectra and chiral symmetry in QCD are still unsolved problems [2]. Since chiral symmetry and nonperturbative phenomena can be easily analyzed in certain models, chiral symmetry and the bound-state spectra in QCD are investigat-features which are expected from QCD, i.e., asymptotic freedom, dynamical symmetry breaking, and dynamical mass generation [4]; it is expected that the properties of the chiral Gross-Neveu model will help us understand the low-energy properties in QCD. Considering the spontaneous breaking of a continuous symmetry does not occur in two space-time dimensions [S], we take the (2 + 1 )-dimensional chiral Gross-Neveu model as an example.The Lagrangian density is given by ed in some models.

We develop Ward-Takahashi identities to include composite fields and utilize them to study gauge symmetry dynamical breaking in Abelian theory. In terms of the equivalence between elementary field description and the composite field description, we obtain a matching condition. The mechanism of mass generation and the mass spectra are investigated in Cornwall-Norton, Jackiw-Johnson, and Schwinger models. The gauge boson masses are in agreement with previous works; meanwhile the composite Higgs boson and decay constant F , which have not been obtained in previous works and other methods, can be easily obtained. It turns out that this approach can be easily applied to study not only the mass generation of fermion and gauge bosons, but also that of composite fields. ͓S0556-2821͑98͒02808-2͔

Chiral Ward-Takahashi identities with composite fields are generalized to finite temperature and applied to investigate the chiral phase transition and phase structure in the (2+ 1)-dimensional chiral Gross-Neveu model. In terms of these identities, the mass spectra of fermions and bound states and the Goldberger-Treiman relation at finite temperature are obtained. The vertex correction between the fermion and bound states a is evaluated beyond the leading order in the 1 / N expansion at zero and finite temperatures. With the aid of the gap equation derived from Ward-Takahashi identities, the phase structure is discussed at zero and finite temperatures. It turns out that (i) at zero temperature, the vertex correction is very small and its influence on the phase structure can be neglected and (ii) at nonzero temperature, the infrared divergence in the vertex correction will make the results of the chiral phase transition obtained at the leading order invalid in next to the leading order and the phase structure is in agreement with Coleman's theorem.