We show that the Aharonov–Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper, we show that this “topological” quantum number amounts to the presence of a background flat potential which rules the behaviour of charges when transported along paths as in the Aharonov–Bohm effect. To confirm these abstract results, we quantize the Dirac field in the presence of a background flat potential and show that the Aharonov–Bohm phase gives an irreducible representation of the fundamental group of the spacetime labelling the charged sectors of the Dirac field. We also show that non-Abelian generalizations of this effect are possible only on spacetimes with a non-Abelian fundamental group.

Dappiaggi, C., Ruzzi, G., Vasselli, E. (2020). Aharonov–Bohm superselection sectors. LETTERS IN MATHEMATICAL PHYSICS, 110(12), 3243-3278 [10.1007/s11005-020-01335-4].

Aharonov–Bohm superselection sectors

Ruzzi G.;
2020-01-01

Abstract

We show that the Aharonov–Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper, we show that this “topological” quantum number amounts to the presence of a background flat potential which rules the behaviour of charges when transported along paths as in the Aharonov–Bohm effect. To confirm these abstract results, we quantize the Dirac field in the presence of a background flat potential and show that the Aharonov–Bohm phase gives an irreducible representation of the fundamental group of the spacetime labelling the charged sectors of the Dirac field. We also show that non-Abelian generalizations of this effect are possible only on spacetimes with a non-Abelian fundamental group.
2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/07 - FISICA MATEMATICA
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Aharonov–Bohm; superselection sectors; quantum field theory
Dappiaggi, C., Ruzzi, G., Vasselli, E. (2020). Aharonov–Bohm superselection sectors. LETTERS IN MATHEMATICAL PHYSICS, 110(12), 3243-3278 [10.1007/s11005-020-01335-4].
Dappiaggi, C; Ruzzi, G; Vasselli, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/264939
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