Remarks on fermion-number violation and premature unitarization in high-energy instanton-induced scattering

We critically discuss recent works in which the premature unitarization mechanism is studied with the inclusion of non-nearest-neighbor interactions or beyond leading order in the energy. We also point out that the nonperturbative valley method gives inconsistent results when applied to fermion-number-violating amplitudes, and we argue that, independently of the mechanism of premature unitarization, the nonperturbative amplitudes which violate the fermion number are always exponentially suppressed