Gross-Neveu model with overlap fermions

We investigate the chiral properties of overlap lattice fermion by using tw o-dimensional Gross-Neveu model coupled with a gauge field. Chiral properti es of this model are similar to those of QCD(4), i.e. the chiral symmetry i s spontaneously broken in the presence of small but finite fermion mass and also there appears the chiral anomaly because of the coupling with the gau ge field. To take into consideration Luscher's extended chiral symmetry, we insert overlap Dirac operator even in the interaction terms so that the wh ole action including them are invariant under the extended chiral transform ation at finite lattice spacing though the interaction terms become nonloca l. We calculate mass of the quasi-Namb-Goldstone boson as a function of the bare fermion mass and two parameters in the overlap formalism and find tha t the quasi-Nambu-Goldstone boson has desired properties as a result of the extended chiral symmetry. Furthermore we examine the PCAC relation and fin d that it is satisfied at finite lattice spacing. Relationship between the anomaly term in the PCAC relation and the U(1) problem is also discussed.