Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Space science journal.

Comment On ‘Lorentz-Invariance and Gauge-Invariance of the Aharonov–Bohm Phase’

P. Enders, permanent address: Ahornallee 11, D-15712 Königs Wusterhausen, Germany

Published Oct 31, 2025• 0 citations
Publisher

Abstract

I present an axiomatic foundation of non-integrable phases of quantum wave functions like the Aharonov–Bohm phase and show the gauge invariance of the phase difference in the Aharonov–Bohm setup in a much simpler manner than in that article by Kholmetskii et al
DOI
10.33140/ssj.02.04.01

Related papers

Lorentz-invariance and gauge-invariance of the Aharonov–Bohm phase

Alexander L. Kholmetskii, O. Missevitch, Tolga Yarman

The European Physical Journal Plus•Feb 18, 2025•2 citations

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

How to test the gauge-invariant non-local quantum dynamics of the Aharonov–Bohm effect

T. Kaufherr

arXiv:1411.2814•Quantum Studies Mathematics and Foundations•Sep 8, 2014•4 citations

Phase (or gauge) invariance and new field-free Aharonov-Bohm effects

Gianfranco Spavieri

The European Physical Journal D•Dec 12, 2005•16 citations

Different ways to the Aharonov–Bohm effect and elucidation of its physical meaning

Alexander L. Kholmetskii, O. Missevitch, Tolga Yarman

We compare different ways to the Aharonov–Bohm (A–B) phase for an electrically charged point-like particle in an electromagnetic field and disclose three mathematically equivalent representations for the A–B phase, which explicitly demonstrate its Lorentz invariance and gauge invariance. Based on these results, we obtain a linear dependence of the wave vector of a moving charged particle on the vector composition of mechanical and electromagnetic momenta, which sheds new light on the physical origin of the A–B effect.

International Journal of Modern Physics A•Mar 30, 2026•0 citations

On the phase of wave function and the gauge invariance in norelativistic quantum mechanics

T. Inagaki

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento•Mar 1, 1984•0 citations
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.
We compare different ways to the Aharonov–Bohm (A–B) phase for an electrically charged point-like particle in an electromagnetic field and disclose three mathematically equivalent representations for the A–B phase, which explicitly demonstrate its Lorentz invariance and gauge invariance. Based on these results, we obtain a linear dependence of the wave vector of a moving charged particle on the vector composition of mechanical and electromagnetic momenta, which sheds new light on the physical origin of the A–B effect.