Implementability of gauge transformations and quantization of fermions in external fields

Abstract

Quantization of fermions in an external soliton field, leading to a representation of the canonical anticommutation relation (CAR), which is inequivalent to the representation connected to the massive Dirac operator, is studied. Classes of gauge and axial gauge transformations that can be unitarily implemented are determined. In the latter case quantization conditions for gauge functions are obtained; integers entering can be interpreted as winding numbers.