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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Consistency of the Aharonov-Bohm effect with quantum theory

Yakir Aharonov, C. K. Au, E. C. Lerner, Jun Liang

Published Feb 1, 1984• 7 citations
Publisher
DOI
10.1007/bf02800257

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Reply to “Comment on ‘Energy-level shift of quantum systems via the scalar electric Aharonov-Bohm effect' ”

R. Y. Chiao, Harold Hart, Michael Scheibner +4 more

We respond to the points raised in the preceding Comment [] on our recent work [], which introduced a theoretical framework for the scalar electric Aharonov-Bohm effect. In this Reply, we take the opportunity to address specific criticisms, by referring to foundational aspects of gauge invariance and time-dependent quantum systems. We explain why the gauging procedure used in the Comment leads to inconsistencies and show that, when applied similarly to the well-established magnetic Aharonov-Bohm effect, it would yield demonstrably incorrect conclusions. Moreover, we highlight the consistency of our results with canonical treatments of the time-dependent Schrödinger equation, and we reaffirm the physicality of energy shifts in field-free regions, an effect observed in the magnetic and predicted in the electric Aharonov-Bohm contexts. We believe that this response contributes to a deeper understanding of the subtleties involved in gauge theory and quantum phase phenomena.

Physical Review A•May 29, 2025•0 citations

Quantum laws and aharonov-bohm effect

P. Bocchieri, A. Loinger

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento•May 1, 1984•2 citations
It has been suggested that the magnetic Aharonov-Bohm effect can be interpreted equally well as being due to a phase shift associated with an electron in an interferometer enclosing a magnetic flux, or as a phase shift associated with the electrons in the solenoid that generates the field. Here the Aharonov-Bohm effect is derived using second-quantized field theory to describe all the electrons as well as the electromagnetic field in a consistent way. The results are in agreement with the usual expression for the Aharonov-Bohm effect when the retardation of the electromagnetic field is negligible, but they predict the possibility of a fractional phase shift when retardation effects are significant.
A field-interaction scheme is introduced for describing the Aharonov-Bohm effect, fully consistent with the principle of relativity. Our theory is based on the fact that local field interactions are present even when a particle moves only in a field-free region. The interaction Lagrangian between a charge and a flux is uniquely constructed from three principles: Lorentz covariance, linearity in the interaction strength, and a correct stationary limit of charge. Our result resolves fundamental questions raised on the standard interpretation of the Aharonov-Bohm effect, concerning its duality with the Aharonov-Casher effect and the equivalence between the potential and the field-interaction models for describing the electromagnetic interaction. Most of all, potential is eliminated in our theory, and all kind of the force-free Aharonov-Bohm effect is understood in a unified framework of the Lorentz-covariant local interaction of electromagnetic fields.
We respond to the points raised in the preceding Comment [] on our recent work [], which introduced a theoretical framework for the scalar electric Aharonov-Bohm effect. In this Reply, we take the opportunity to address specific criticisms, by referring to foundational aspects of gauge invariance and time-dependent quantum systems. We explain why the gauging procedure used in the Comment leads to inconsistencies and show that, when applied similarly to the well-established magnetic Aharonov-Bohm effect, it would yield demonstrably incorrect conclusions. Moreover, we highlight the consistency of our results with canonical treatments of the time-dependent Schrödinger equation, and we reaffirm the physicality of energy shifts in field-free regions, an effect observed in the magnetic and predicted in the electric Aharonov-Bohm contexts. We believe that this response contributes to a deeper understanding of the subtleties involved in gauge theory and quantum phase phenomena.