Chiral symmetry, Ward-Takahashi identities and mass spectra in a (2+1)-dimensional four-fermion model

Abstract

Ward-Takahashi identities with composite fields are utilized to investigate fermion mass generation, bound state spectra in a (2+1)-dimensional four-fermion model. When chiral symmetry is both dynamically and explicitly broken, the Goldberger-Treiman relation is approximately valid in the case of small explicit breaking, and the massive pi bound state and PCAC, which are independent of the 1/N expansion or chiral perturbative expansion, are obtained.