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arxiv: 2605.20499 · v1 · pith:AZOCUQ3Enew · submitted 2026-05-19 · ⚛️ physics.gen-ph

Beyond minimal coupling for charged scalars? Modified electrodynamics and London-penetration tests

F. Minotti , G. Modanese This is my paper

Pith reviewed 2026-05-21 06:00 UTC · model grok-4.3

classification ⚛️ physics.gen-ph
keywords modified electrodynamicsLondon penetration depthcharged scalar fieldsbosonic condensatessuperconductivitygauge invarianceAharonov-Bohm electrodynamicsGinzburg-Landau theory
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The pith

A modified linear coupling of electromagnetic fields to globally conserved currents predicts that the London penetration depth in bosonic charged condensates is rescaled by 1/√2.

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

Standard minimal coupling to the vector potential works for fermions but produces an inconsistency for scalar fields because the interaction term linear in A does not match the Noether current of the interacting theory. The authors replace it with a direct linear term A_μ J^μ where J^μ is only globally conserved, which requires dropping local gauge invariance in the electromagnetic sector and using an extended Aharonov-Bohm-type electrodynamics. Under this change the Ginzburg-Landau description of a charged bosonic condensate yields a magnetic penetration depth reduced by a factor of √2 while the type-I/type-II classification and other qualitative features survive after a corresponding rescaling of the GL parameter. The authors compare independent optical and magnetic measurements of the penetration depth in several superconductors and find that the observed ratio is often close to √2, as required by the modified theory.

Core claim

For bosonic charged condensates the modified framework predicts a rescaled magnetic penetration depth λ → λ/√2 while leaving other key qualitative features of superconducting electrodynamics and the type-I/type-II distinction unchanged up to an equivalent rescaling of the GL parameter.

What carries the argument

The linear coupling A_μ J^μ to a globally conserved current J^μ, introduced inside an extended electrodynamics that relaxes local gauge invariance.

If this is right

  • The distinction between type-I and type-II superconductors remains intact after a rescaling of the Ginzburg-Landau parameter.
  • All other qualitative features of London and Ginzburg-Landau electrodynamics are preserved under the same rescaling.
  • Consistency checks become possible by comparing independently measured optical and magnetic penetration depths in the same material.
  • The framework applies specifically to bosonic condensates and leaves fermionic cases unchanged.

Where Pith is reading between the lines

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

  • If confirmed, the rescaling would alter the inferred superfluid density extracted from magnetic measurements in bosonic systems.
  • The same modified coupling could be tested in other charged scalar systems such as charged Bose-Einstein condensates or exciton-polariton condensates.
  • The relaxation of local gauge invariance might require re-examination of flux quantization or Aharonov-Bohm phases in superconducting circuits.

Load-bearing premise

The electromagnetic interaction must be written as a direct linear coupling to a globally conserved current rather than the usual minimal-coupling term that preserves local gauge invariance.

What would settle it

A precise measurement showing that the ratio of optical penetration depth (from superfluid spectral weight) to magnetic penetration depth (from μSR or microwave methods) equals exactly 1 in Nb or YBCO would contradict the predicted √2 rescaling.

read the original abstract

While standard minimal coupling works well for Dirac fermions, its application to scalar fields features a known ``peculiarity'': the term linear in $A_\mu$ does not coincide with the conserved Noether current of the interacting theory. We recently proposed choosing a different principle for electromagnetic interactions, namely a linear coupling $A_\mu J^\mu$ with $J^\mu$ a (globally) conserved current, accepting the consequence that one must abandon full local gauge invariance in the electromagnetic sector and adopt an extended electrodynamics (of Aharonov--Bohm type) that can couple consistently to non-locally-conserved currents. We present the physical motivations offered for proposing the modified coupling and discuss general consequences of reducing gauge invariance. We then focus on the central condensed-matter claim: for bosonic charged condensates, the modified framework predicts a rescaled magnetic penetration depth $\lambda \to \lambda/\sqrt{2}$, while leaving other key qualitative features of superconducting electrodynamics and the type-I/type-II distinction unchanged (up to an equivalent rescaling of the GL parameter). Finally, we analyze experimental data for a London-length consistency check based on independent measurements of the ratio $n_s/m^\ast$ between carrier density and effective mass. We compare for five materials an ``optical'' penetration depth $\lambda_{\mathrm{opt}}$ inferred from IR/THz superfluid spectral weight with a ``magnetic'' depth $\lambda_{\mathrm{mag}}$ obtained independently (LE-$\mu$SR, TF-$\mu$SR, microwave methods, etc.). Data for Nb, YBCO and Ba(Fe,Co)$_2$As$_2$ confirm the hypothesis $\lambda_{\mathrm{opt}}>\lambda_{\mathrm{mag}}$, with a ratio not far from 1.4; data for Pb are inconclusive while data for MgB$_2$ indicate $\lambda_{\mathrm{opt}}\simeq\lambda_{\mathrm{mag}}$ as predicted by the standard theory.

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

2 major / 2 minor

Summary. The paper proposes replacing standard minimal coupling for charged scalar fields with a linear coupling A_μ J^μ where J^μ is globally conserved, requiring abandonment of full local gauge invariance in favor of an extended Aharonov-Bohm-type electrodynamics. For bosonic charged condensates this yields a rescaled London penetration depth λ → λ/√2 while preserving other qualitative features of superconducting electrodynamics up to equivalent rescaling of the Ginzburg-Landau parameter. The authors perform a consistency check by comparing optical penetration depths (from IR/THz superfluid spectral weight) with independently measured magnetic penetration depths in five materials, reporting that Nb, YBCO and Ba(Fe,Co)₂As₂ show λ_opt/λ_mag ratios near √2.

Significance. If the central claim holds, the work supplies a concrete, falsifiable prediction for a modified electromagnetic coupling in scalar condensates together with an explicit multi-material experimental test using independent λ_opt and λ_mag determinations. The provision of a parameter-free rescaling factor and the focus on a measurable ratio constitute strengths that would, if validated, motivate re-examination of minimal coupling for bosons.

major comments (2)
  1. [London-length consistency check] The extraction of λ_opt from superfluid spectral weight is performed with the standard minimal-coupling London relation J = −(n_s e²/m)A. In the modified framework the constitutive relation between current and vector potential, together with the inhomogeneous Maxwell equations, is altered by the linear coupling to a globally conserved current. Consequently the published λ_opt values cannot be inserted unchanged into the ratio test; a re-derivation of the optical response under the new electrodynamics is required before any numerical comparison to λ_mag can be interpreted as support for the √2 rescaling. This issue is load-bearing for the central empirical claim.
  2. [Derivation of the rescaling] The rescaling factor √2 is stated to follow directly from the modified coupling, yet the manuscript provides no explicit derivation of the modified London equation or the resulting penetration depth in terms of the new constitutive relation and extended Maxwell equations. Without these steps it is impossible to verify that other qualitative features (type-I/type-II distinction, GL parameter rescaling) remain unchanged except for the overall factor.
minor comments (2)
  1. [Abstract] The abstract reports that data for Nb, YBCO and Ba(Fe,Co)₂As₂ confirm the hypothesis with a ratio “not far from 1.4”, but does not quote the individual measured ratios or their uncertainties; adding these numbers would allow readers to judge the quantitative agreement.
  2. [Theoretical framework] Notation for the globally conserved current J^μ versus the Noether current should be introduced once and used consistently throughout the theoretical sections to avoid ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The two major comments identify important gaps in the presentation that we will address through targeted revisions.

read point-by-point responses

  1. Referee: [London-length consistency check] The extraction of λ_opt from superfluid spectral weight is performed with the standard minimal-coupling London relation J = −(n_s e²/m)A. In the modified framework the constitutive relation between current and vector potential, together with the inhomogeneous Maxwell equations, is altered by the linear coupling to a globally conserved current. Consequently the published λ_opt values cannot be inserted unchanged into the ratio test; a re-derivation of the optical response under the new electrodynamics is required before any numerical comparison to λ_mag can be interpreted as support for the √2 rescaling. This issue is load-bearing for the central empirical claim.

    Authors: We agree that the published λ_opt values were extracted under the standard minimal-coupling assumption and cannot be used unchanged. In the revised manuscript we will derive the optical response (conductivity and superfluid spectral weight) from the linear coupling A_μ J^μ together with the modified inhomogeneous Maxwell equations. This will yield a consistent expression for λ_opt within the new framework, allowing a properly interpreted comparison to the independently measured λ_mag. revision: yes

  2. Referee: [Derivation of the rescaling] The rescaling factor √2 is stated to follow directly from the modified coupling, yet the manuscript provides no explicit derivation of the modified London equation or the resulting penetration depth in terms of the new constitutive relation and extended Maxwell equations. Without these steps it is impossible to verify that other qualitative features (type-I/type-II distinction, GL parameter rescaling) remain unchanged except for the overall factor.

    Authors: The referee correctly observes that the manuscript states the √2 rescaling without supplying the intermediate steps. We will insert a dedicated derivation section that begins from the modified constitutive relation, obtains the London equation, and extracts the penetration depth. The same derivation will explicitly confirm that the type-I/type-II distinction and other qualitative features survive up to a rescaled Ginzburg-Landau parameter. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper introduces the modified linear coupling A_μ J^μ (with globally conserved J^μ) as an explicit premise motivated by the known peculiarity of minimal coupling for scalars, then derives the λ → λ/√2 rescaling as a direct consequence of the resulting extended electrodynamics and constitutive relations. This is a model-level consequence rather than a fit or self-referential definition; the data comparison is presented only as a post-derivation consistency check using independently measured quantities. Self-citations to the authors' prior proposal exist but are not load-bearing for the present derivation, which rests on the stated equations of the modified theory. No quoted step reduces the central prediction to its inputs by construction, and the framework remains self-contained against external benchmarks for the purpose of this analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The framework introduces one new coupling principle and one new entity (extended electrodynamics) while relying on standard assumptions about global current conservation and the validity of the London and Ginzburg-Landau descriptions.

axioms (2)
  • ad hoc to paper Electromagnetic interactions must be realized by a linear coupling A_μ J^μ where J^μ is a globally conserved current.
    This is the alternative principle chosen instead of minimal coupling; it is stated in the abstract as the basis for the modified framework.
  • ad hoc to paper Full local gauge invariance can be abandoned in the electromagnetic sector while still obtaining consistent coupling to non-locally-conserved currents.
    Explicitly accepted consequence of the new coupling choice.
invented entities (1)
  • Extended electrodynamics of Aharonov-Bohm type no independent evidence
    purpose: To allow consistent coupling to currents that are not locally conserved once local gauge invariance is dropped.
    Introduced to replace standard Maxwell electrodynamics under the new coupling rule.

pith-pipeline@v0.9.0 · 5900 in / 1686 out tokens · 31488 ms · 2026-05-21T06:00:58.128435+00:00 · methodology

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Reference graph

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