Significance of Electromagnetic Potentials in the Quantum Theory
Open accessAbstract
In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish. We shall then discuss possible experiments to test these conclusions; and, finally, we shall suggest further possible developments in the interpretation of the potentials.
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The discovery of the AB effect confirmed the physical reality of gauge potentials and the nonlocality of gauge interactions.
“The AB effect covers a group of phenomena associated with the path-dependent phase factors for particles traveling in a field-free region, but with irremovable gauge potential , the discovery of which confirmed the physical reality of gauge potentials and the nonlocality of gauge interactions56,57.”
From Non-Abelian gauge field optics (2019) · cites this paper as [56]
Section 5 says potentials can be physically effective for electrons in field-free regions, supporting that part of the claim. But it describes nonlocal interaction as one possible theoretical direction, alongside retaining a local theory; it does not say the effect confirmed nonlocal gauge interactions. Section 3 also says no direct experiment had yet confirmed the predicted effect. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe AB effect covers phenomena associated with path-dependent phase factors for particles traveling in a field-free region but with irremovable gauge potential.
“The AB effect covers a group of phenomena associated with the path-dependent phase factors for particles traveling in a field-free region, but with irremovable gauge potential , the discovery of which confirmed the physical reality of gauge potentials and the nonlocality of gauge interactions56,57.”
From Non-Abelian gauge field optics (2019) · cites this paper as [56]
The missing charge should not be identified with the concept of an emergent quasiparticle.
“Wedemonstrate that the missing charge should not be identified with the concept of an emergent quasiparticle by showing that ∆ q ℏ ∮ A · d l does not correspond to the Aharonov-Bohm phase [2] acquired as the probe traverses a loop in space.”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [2]
The Aharonov-Bohm effect is a phenomenon in which charged particles feel electromagnetic potentials even in regions with no magnetic field.
“Aharonov-Bohmov efekt [2] je fenomen u kojem nabijene ˇ cestice osje´ caju utjecaj elektromagnetskih potencijala ˇ cak i u podruˇ cjima gdje nema magnetskog polja.”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [2]
Bi2Se3 and related materials have been proposed as three-dimensional topological insulators with a single Dirac cone on the surface and verified by angle-resolved photoemission spectroscopy experiments.
“3D topological insulators with the simplest possible surface states consisting of a single Dirac cone, on the other hand, have been proposed theoretically [10] in stoichiometric compounds Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 , and topological surface states have been observed independently by angle-resolved photoemission spectroscopy (ARPES) experiments in Bi 2 Se 3 [11].”
From Aharonov–Bohm interference in topological insulator nanoribbons (2010) · cites this paper as [11]
Bi2Se3 has a simple band structure with a single Dirac cone on the surface and a large non-trivial bulk gap of 0.3 eV.
“Among these materials, Bi 2 Se 3 , a narrow gap semiconductor for IR detectors and thermoelectric applications [13], has a simple band structure with a single Dirac cone on the surface and a large non-trivial bulk gap of 0.3eV [10, 11].”
From Aharonov–Bohm interference in topological insulator nanoribbons (2010) · cites this paper as [11]
Neither bulk-related effect could result in B-periodicity over the large field range in this experiment; therefore the AB effect in Bi2Se3 nanoribbons indisputably manifests the existence of conducting surface states.
“Nevertheless, neither of these bulk-related effects could result in B-periodicity over the large field range in this experiment. Therefore, the AB effect in Bi 2 Se 3 nanoribbons indisputably manifests the existence of the conducting surface states”
From Aharonov–Bohm interference in topological insulator nanoribbons (2010) · cites this paper as [11]
The conservation of total angular momentum, Eq. (3.42), links the spin Hall effect of light to the transverse Imbert-Fedorov shift.
“The conservation of the total angular momentum, Eq. (3.42), links the spin Hall effect of light to another remarkable phenomenon - the transverse Imbert-Fedorov shift [24,27,99 -118].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [100]
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- Authors
- Aharonov, Y., & Bohm, D.
- Affiliations
- University of Bristol (GB)
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1959-08-01
- Volume
- 115
- Issue
- 3
- Pages
- 485-491
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2028948400
- Cited by
- 6,996
- References
- 7
- Citations by year
- 2026: 173 · 2025: 236 · 2024: 249 · 2023: 360 · 2022: 220 · 2021: 232 · 2020: 292 · 2019: 309 · 2018: 207 · 2017: 194 · 2016: 227 · 2015: 179 · 2014: 204 · 2013: 217 · 2012: 196
- FWCI
- 9.86
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- electromagnetic potentials, quantum mechanics, charged particles, Aharonov-Bohm effect, experimental testing
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