# Quantized vector potential and alternative views of the magnetic Aharonov-Bohm phase shift

@article{Pearle2017QuantizedVP, title={Quantized vector potential and alternative views of the magnetic Aharonov-Bohm phase shift}, author={Philip Mark Pearle and Anthony Rizzi}, journal={Physical Review A}, year={2017}, volume={95}, pages={052124} }

We give a complete quantum analysis of the Aharonov-Bohm (AB) magnetic phase shift involving three entities: the electron, the charges constituting the solenoid current, and the vector potential. The usual calculation supposes that the solenoid's vector potential may be well approximated as classical. The AB shift is then acquired by the quantized electron moving in this vector potential. Recently, Vaidman presented a semiclassical calculation [L. Vaidman, Phys. Rev. A 86, 040101 (2012)], later…

## 11 Citations

Classical nonlocality and the Aharonov-Bohm effect

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The Aharonov-Bohm effect is a quantum mechanical phenomenon in which it is widely accepted that the observed Aharonov-Bohm phase can be explained by assuming that the magnetic field can produce…

Surprising predictions of the electromagnetic angular momentum

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In the context of the Aharonov-Bohm effect, it is well-known that the local action of the vector potential or the non-local action of the magnetic field are properties attributable to quantum…

Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond

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Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm,…

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This paper mathematically model the operation of the electromagnetic grid, especially in regard to the functional role of atomic orbitals of dipole-bound delocalized electrons, and uses a simplified version of the many-body problem to analytically solve the macro-quantum wave equation.

Aharonov-Bohm effect with an effective complex-valued vector potential

- Physics
- 2021

I. L. Paiva , 2, 3 Y. Aharonov, 2, 4 J. Tollaksen, 2 and M. Waegell 2 Schmid College of Science and Technology, Chapman University, Orange, California 92866, USA Institute for Quantum Studies,…

Geometric phases and the Sagnac effect: Foundational aspects and sensing applications

- Physics
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Geometric phase is a key player in many areas of quantum science and technology. In this review article, we outline several foundational aspects of quantum geometric phases and their relations to…

Local Description of the Aharonov–Bohm Effect with a Quantum Electromagnetic Field

- Physics
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In the seminal works from Santos and Gozalo (Europhys Lett 45:418, 1999) and Marletto and Vedral (Phys Rev Lett 125:040401, 2020), it is shown how the Aharonov–Bohm effect can be described as the…

Gauge-Underdetermination and Shades of Locality in the Aharonov–Bohm Effect

- Mathematics, Physics
- 2021

I address the view that the classical electromagnetic potentials are shown by the Aharonov–Bohm effect to be physically real (which I dub: ‘the potentials view’). I give a historico-philosophical…

Dimensional scaffolding of electromagnetism using geometric algebra

- Physics
- 2020

Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the…

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