  The basic aspects of the Aharonov-Bohm effect can be summarized by the remark
that wavefunctions become sections of a line bundle with a flat connection
(that is, a "flat potential"). Passing at the level of quantum field theory in
curved spacetimes, we study the Dirac field interacting with a classical
(background) flat potential and show that it can be interpreted as a
topological sector of the observable net of free Dirac field. On the converse,
starting from a topological sector we reconstruct a classical flat potential,
interpreted as an interaction of a Dirac field. This leads to a description of
Aharonov-Bohm-type effects in terms of localized observables.
