Off-topic for aiqbench
This story was gathered from a source we follow but falls outside AI and quantum coverage, so there is no aiqbench take for it.
The gauge freedom in the Aharonov-Casher theorem: The problem in two and one dimensions
arXiv:2509.24028v3 Announce Type: replace Abstract: In this note, we investigate the role of gauge freedom in the Aharonov-Casher theorem in one and two dimensions. In particular, we analyze the asymptotic behavior of the gauge freedom. We show that in two-dimensional space the gauge field is uniquely determined, whereas in one dimensional space a residual gauge freedom allows for an infinite family of equivalent gauges. This freedom is determined by a constant k. However, the number $k$ must be restricted in order to guarantee the existence of a normalizable zero mode. This restriction is determined by the inequality $|k| < \frac{1}{2} \int dx B(x)$, where $B(x)$ is a scalar field localized in a finite region of space. We show that this condition is equivalent to the gauge field taking opposite-sign values at $+\infty$ and $-\infty$. Finally, we illustrate these results with an explicit example.
Abstract:In this note, we investigate the role of gauge freedom in the Aharonov-Casher theorem in one and two dimensions. In particular, we analyze the asymptotic behavior of the gauge freedom. We show that in two-dimensional space the gauge field is uniquely determined, whereas in one dimensional space a residual gauge freedom allows for an infinite family of equivalent gauges. This freedom is determined by a constant k. However, the number $k$ must be restricted in order to guarantee the existence of a normalizable zero mode. This restriction is determined by the inequality $|k| < \frac{1}{2} \int dx B(x)$, where $B(x)$ is a scalar field localized in a finite region of space. We show that this condition is equivalent to the gauge field taking opposite-sign values at $+\infty$ and $-\infty$. Finally, we illustrate these results with an explicit example.
6 pages, one figure. To be published in Revista Mexicana de Física
arXiv:2509.24028 [quant-ph]
(or arXiv:2509.24028v3 [quant-ph] for this version)
From: Lucas Sourrouille Mr. [view email] [v1] Sun, 28 Sep 2025 18:44:32 UTC (8 KB) [v2] Sun, 5 Jul 2026 01:44:11 UTC (30 KB) [v3] Sun, 11 Oct 2026 03:08:24 UTC (33 KB)
Full text under the publisher's open licence · 191 words
Related coverage
Lattice-Based Cryptography Explained
Quantum Zeitgeist · Aug 15, 2026
The Entangled Dimensions of Decision Theory
LessWrong · Jul 30, 2026
Wells Fargo Researchers Quantify Gauge Redundancy in Variational Quantum Circuits
Quantum Zeitgeist · Jul 23, 2026
On the relation between perspective-neutral, algebraic, and effective quantum reference frames
Quantum Journal · Aug 20, 2026