Background potentials and superselection sectors

Ezio Vasselli
November 29, 2018
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.
open access link
@article{Vasselli:2018fns, author = "Vasselli, Ezio", title = "{Background potentials and superselection sectors}", year = "2018", eprint = "1811.12121", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1811.12121;%%" }

Quantum field theory, Superselection Theory