Lattice QCD with the Overlap Fermions at Strong Gauge Coupling

We generalize overlap fermion by Narayanan and Neuberger by introducing a hopping parameter t. This lattice fermion has desirable properties as the original overlap fermion. We expand "Dirac" operator of this fermion in powers of t. Higher-order terms of t are long-distance terms and this t-expansion is a kind of the hopping expansion. It is shown that the Ginsparg-Wilson relation is satisfied at each order of t. We show that this t-expansion is useful for study of the strong-coupling gauge theory. We apply this formalism to the lattice QCD and study its chiral phase structure at strong coupling. We find that there are (at least) two phases one of which has desired chiral properties of QCD. Possible phase structure of the lattice QCD with the overlap fermions is proposed.