Ward-takahashi identities and mass spectra in (2 + 1) dimensional SU(2) four-Fermi model

Ward-Takahashi identities with composite fields are utilized to investigate (2 + 1) dimensional model with SU(2) four-Fermion couplings. When SU(2) chiral symmetry is both explicitly and dynamically broken, fermion mass is dynamically generated and mass spectra of the bound states are obtained. The properties of vector and axial-vector currents are discussed. It turns out that the bound state πα acquires a mass and the axial-vector current is partially conserved, and the Goldberger-Treiman relation is approximately valid in the case of small fermion current masses