Pion mass and the PCAC relation in the overlap fermion formalism: Gauged Gross-Neveu model on a lattice

We investigate chiral properties of the overlap lattice fermion by using so lvable model in two dimensions, the gauged Gross-Neveu model. Ln this model , the chiral symmetry is spontaneously broken in the presence of small but finite fermion mass. We calculate the quasi-Nambu-Goldstone (NG) boson mass as a function of the bare fermion mass a-nd two parameters in the overlap formula. We find that the quasi-NC boson mass has desired properties as a r esult of the extended chiral symmetry found by Luscher. We also examine the PCAC relation and find that it is satisfied in the continuum limit. Compar ison between the overlap and Wilson lattice fermions is made. (C) 1999 Publ ished by Elsevier Science B.V. All rights reserved.