Anomalies without massless particles

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Abstract
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 arises from nonadiabatic behavior that compensates for the absence of massless modes. On the other hand, for localized instantonlike 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.
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