Anomalies without Massless Particles

Baryon and lepton number in the standard model are violated by anomalies, even though the fermions are massive. This problem is studied in the context of a two dimensional model. In a uniform background field, fermion production arise from non-adiabatic behavior that compensates for the absence of massless modes. On the other hand, for localized instanton-like configurations, there is an adiabatic limit. In this case, the anomaly is produced by bound states which travel across the mass gap. The sphaleron corresponds to a bound state at the halfway point.