Background potentials and superselection sectors
arXiv:1811.12121 · doi:10.1016/j.geomphys.2019.02.001
Abstract
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.
16 pages; a report on a work in progress with C. Dappiaggi and G. Ruzzi; in the new version, added references and corrected misprints. To appear on Journal of Geometry and Physics