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arxiv: 2511.11120 · v2 · submitted 2025-11-14 · 🪐 quant-ph · hep-th· math-ph· math.MP

Magnetic flux and its topological effects in Aharonov-Bohm effect

Manvendra Somvanshi , D. Jaffino Stargen This is my paper

Pith reviewed 2026-05-17 22:17 UTC · model grok-4.3

classification 🪐 quant-ph hep-thmath-phmath.MP
keywords Aharonov-Bohm effecttopological phase shiftconfiguration space puncturemagnetic fluxquantum interferencepunctured planenonlocal phasetopology of R^2 minus point
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The pith

The confined magnetic field punctures the particle's configuration space, producing the Aharonov-Bohm phase shift through topology alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that a classical magnetic field confined inside a region creates a puncture, or hole, at the origin of the two-dimensional plane in which a charged quantum particle moves. Because the particle cannot enter the hole, its available configuration space becomes the punctured plane rather than the full plane. The quantum state of the particle therefore responds to this change in topology and accumulates a phase when its path winds around the puncture. The accumulated phase equals the enclosed flux in natural units and directly accounts for the observed shift in interference fringes. A reader would care because the account replaces the apparent nonlocality of the effect with a concrete geometric modification of the space the particle inhabits.

Core claim

The role of the confined magnetic field is to impart a puncture in the configuration space, R^2, of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space, R^2-{0}, corresponding to the charge.

What carries the argument

The puncture that turns the configuration space R^2 into the topologically distinct space R^2 minus a point, thereby forcing any closed path that encircles the point to produce a flux-dependent phase in the wave function.

If this is right

  • The measured phase depends only on the total enclosed flux and the winding number of the path around the puncture.
  • The interference pattern is altered even when the particle never enters the region containing the magnetic field.
  • The standard vector-potential description outside the solenoid is not required to obtain the exact phase value.
  • Any gauge-invariant observable built from paths that share the same winding number will exhibit the same flux dependence.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same puncture mechanism may supply a topological account for other confined-flux phenomena that appear nonlocal in ordinary treatments.
  • It suggests constructing analog systems, such as lattices with artificial defects, to isolate and measure the purely topological contribution to phase shifts.
  • If correct, the view implies that the effect should survive in any quantum theory whose configuration space can be punctured while preserving the same fundamental group.

Load-bearing premise

The flux-dependent phase is generated entirely by the topological change in configuration space and does not rely on the usual vector-potential mechanism outside the field region.

What would settle it

An explicit solution of the Schrödinger equation on the full plane R^2 with the same confined flux that yields a phase different from the topological prediction, or an interference experiment in which the phase remains unchanged after the puncture is removed while the flux is kept fixed.

Figures

Figures reproduced from arXiv: 2511.11120 by D. Jaffino Stargen, Manvendra Somvanshi.

Figure 1
Figure 1. Figure 1: FIG. 1: A schematic overview of the Aharonov-Bohm setup, [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
read the original abstract

The Aharonov-Bohm effect is a physical phenomenon in which the quantum state of a charged particle acquires a phase shift that is directly proportional to the magnetic flux, $\Phi$, due to a (classical) magnetic field, ${\mathbf B}$, which is confined in a spatial region from which the magnetic field cannot escape. Even though the charged particle is not allowed to interact with the magnetic field, it accumulates a phase shift that affects the interference pattern produced. Not surprisingly, this apparent nonlocality is puzzling and counter intuitive. In this work, we provide an explanation that explains the physics underlying this apparent nonlocality. We find that the role of the confined magnetic field is to impart a puncture in the configuration space, $\mathbb{R}^2$, of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space, $\mathbb{R}^2-\{0\}$, corresponding to the charge.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript argues that the Aharonov-Bohm effect arises because a confined magnetic field punctures the configuration space R^2 of a charged particle, so that the quantum state acquires its flux-dependent phase shift solely by responding to the modified topology of R^2 minus a point.

Significance. If the central claim were established by an explicit derivation, the work would supply a topological account of the apparent nonlocality in the Aharonov-Bohm effect and clarify the role of multiply-connected configuration spaces in quantum mechanics. The present text, however, offers only a conceptual statement without deriving the precise phase value from topology alone.

major comments (1)
  1. [Abstract] Abstract: the statement that the particle 'acquires the phase shift due to its response to the modified topology of the configuration space, R^2-{0}' does not derive the specific proportionality to the enclosed flux Φ. The fundamental group π1(R^2-{0}) ≅ Z permits arbitrary flat U(1) connections; nothing in the topology itself fixes the holonomy angle to 2π Φ/Φ0 without reintroducing a connection or an equivalent integral of the vector potential.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and for identifying a key point about the explicit derivation of the phase. We respond to the major comment below and indicate how we will strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that the particle 'acquires the phase shift due to its response to the modified topology of the configuration space, R^2-{0}' does not derive the specific proportionality to the enclosed flux Φ. The fundamental group π1(R^2-{0}) ≅ Z permits arbitrary flat U(1) connections; nothing in the topology itself fixes the holonomy angle to 2π Φ/Φ0 without reintroducing a connection or an equivalent integral of the vector potential.

    Authors: We agree that the fundamental group π₁(ℝ² ∖ {0}) ≅ ℤ classifies homotopy classes but does not by itself select a unique holonomy; any flat U(1) connection is topologically allowed. In the manuscript the confined flux Φ plays a dual role: it creates the puncture that changes the topology of the configuration space and, through the associated vector potential, fixes the specific circulation ∮ A · dl = Φ that determines the holonomy 2π Φ / Φ₀. The topological modification accounts for the nonlocal character of the effect, because the wave function must be single-valued on the multiply connected domain. We acknowledge that the present abstract is concise and does not spell out this relation explicitly. We will therefore revise the abstract to distinguish the topological origin of nonlocality from the flux-dependent value of the holonomy and will add a short paragraph in the main text that recalls how the line integral of A yields the phase on the punctured plane. revision: yes

Circularity Check

0 steps flagged

No significant circularity; topological reinterpretation does not reduce to input by construction

full rationale

The paper's central claim is that the confined B field punctures R^2, after which the quantum state acquires the AB phase shift solely by responding to the topology of R^2-{0}. This is an interpretive explanation rather than a derivation chain containing equations or parameters that are fitted and then renamed as predictions. No self-citations, ansatzes, or uniqueness theorems are invoked in the provided text to bear the load of the flux proportionality. The argument does not equate the observed phase to its own inputs by definition; it simply attributes the known effect to the puncture. While the topology alone permits arbitrary holonomies and does not fix the specific value 2πΦ/Φ0 without additional structure, this is a question of explanatory completeness or correctness, not circularity per the enumerated patterns. The derivation is self-contained as a conceptual reframing and receives score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the domain assumption that quantum states in multiply-connected spaces acquire phases determined by topology, together with the ad-hoc identification of the magnetic flux tube as a puncture. No free parameters or new entities with independent evidence are introduced.

axioms (1)
  • domain assumption Quantum mechanics on a multiply connected configuration space produces a phase shift determined by the topology of the space.
    Invoked to link the puncture directly to the observed phase without further derivation.
invented entities (1)
  • Puncture in configuration space no independent evidence
    purpose: To represent the effect of the confined magnetic flux as a topological defect that changes R^2 into R^2 minus a point.
    Postulated to explain the nonlocality; no independent falsifiable prediction is given outside the standard Aharonov-Bohm phase.

pith-pipeline@v0.9.0 · 5479 in / 1427 out tokens · 35883 ms · 2026-05-17T22:17:50.667901+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

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    Therefore, the charged particle responds only to the modified topology of its configuration space, which is R2 − { 0}

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