Manifestly gauge covariant treatment of lattice chiral fermions. II

We propose a formulation of chiral fermions on a lattice, on the basis of a lattice extension of the covariant regularization scheme in continuum field theory. The species doublers do not emerge. The real part of the effective action is just one-half of that of Dirac-Wilson fermion and is always gauge invariant even with a finite lattice spacing. The gauge invariance of the imaginary part, on the other hand, sets a severe constraint that is a lattice analog of the gauge anomaly-free condition. For real gauge representations, the imaginary part identically vanishes and the gauge invariance becomes exact.