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arxiv: 2606.22050 · v2 · pith:J4WBZQD2new · submitted 2026-06-20 · ✦ hep-th

Hamiltonian formulation of Carrollian Maxwell theory in Deformed Light-cone Kaluza-Klein-like Null reduction

Limin Zeng This is my paper

Pith reviewed 2026-06-26 11:44 UTC · model grok-4.3

classification ✦ hep-th
keywords Carrollian Maxwell theorynull reductionKaluza-Klein reductionHamiltonian formulationgauge symmetryBargmann backgroundlight-cone coordinates
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The pith

Kaluza-Klein-like null reduction of a complex Maxwell field in a Bargmann deformed light-cone background produces both magnetic and electric Carrollian Maxwell theories while preserving gauge symmetry.

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

The paper shows how to derive Carrollian Maxwell theories from a higher-dimensional setup by reducing a complex Maxwell field along a null direction in a specially deformed light-cone geometry. The reduction is performed so that the U(1) Gauss constraint remains first-class at every step, which keeps the Hamiltonian formulation gauge invariant. Different choices of field scalings recover the standard magnetic and electric Carrollian versions and also generate new variants that include an extra scalar field appearing either coupled or decoupled. This demonstrates that the method can access a wider range of Carrollian theories than earlier approaches.

Core claim

Performing Kaluza-Klein-like null reduction of a complex Maxwell field in a Bargmann deformed light-cone background with manifest gauge symmetry yields both magnetic and electric Carrollian Maxwell theories. The procedure preserves a first-class U(1) Gauss constraint throughout the Carrollian limit, so gauge invariance is maintained in the Hamiltonian formulation. By choosing different scalings one obtains the standard magnetic Carrollian theory and the electric Carrollian theory; in addition a scalar field can appear in the resulting theory in a coupled or decoupled way.

What carries the argument

The Kaluza-Klein-like null reduction applied to a complex Maxwell field inside a Bargmann deformed light-cone background, with scalings chosen so that the U(1) Gauss constraint stays first-class.

If this is right

  • Gauge invariance remains intact in the Hamiltonian formulation of the obtained Carrollian theories.
  • A scalar field can enter the Carrollian theory either coupled to the Maxwell sector or decoupled from it.
  • The same reduction procedure can generate both the magnetic and the electric Carrollian Maxwell theories from one starting setup.
  • The method supplies an explicit working example for applying the deformed light-cone null reduction to gauge theories.

Where Pith is reading between the lines

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

  • The same background and scaling technique could be tried on non-Abelian gauge fields to produce Carrollian Yang-Mills theories.
  • The decoupled scalar that appears for some scalings may correspond to a new degree of freedom whose Carrollian dynamics has not yet been explored in the literature.
  • Varying the deformation parameter of the light-cone background might produce still other Carrollian limits that interpolate between magnetic and electric regimes.

Load-bearing premise

The chosen Bargmann deformed light-cone background together with the selected field scalings keep the U(1) Gauss constraint first-class and produce consistent Carrollian theories without extra inconsistencies.

What would settle it

An explicit reduction calculation that shows the Gauss constraint becoming second-class or that the resulting equations fail to match the known Carrollian Maxwell dynamics under the stated scalings would falsify the construction.

Figures

Figures reproduced from arXiv: 2606.22050 by Limin Zeng.

Figure 1
Figure 1. Figure 1: FIG. 1: Workflow of deformed light-cone KK-like null [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
read the original abstract

We construct magnetic and electric Carrollian Maxwell theories by performing Kaluza-Klein-like null reduction of a complex Maxwell field in a Bargmann deformed light-cone background with manifest gauge symmetry. The procedure preserves a first-class U(1) Gauss constraint throughout the Carrollian limit. Gauge invariance is therefore maintained in our Hamiltonian formulation. By choosing different scalings, we obtain standard magnetic Carrollian theory and electric Carrollian theory. However, a scalar field could appear in the Carrollian theory in a coupled or decoupled way, which has not been found by previous methods. This result fully reveals the diversity of Carrollian theories accessible through the deformed light-cone Kaluza-Klein-like null reduction method. Furthermore, our work provides an explicit example of the correct application of this approach, thereby broadening the scope of its applicability to gauge theories.

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 constructs magnetic and electric Carrollian Maxwell theories via a Kaluza-Klein-like null reduction of a complex Maxwell field on a Bargmann-deformed light-cone background. It asserts that the reduction preserves a first-class U(1) Gauss constraint and manifest gauge invariance in the Hamiltonian formulation; different scalings are stated to recover the standard magnetic and electric Carrollian theories, with optional scalar coupling that prior methods did not produce.

Significance. If the explicit reduction steps and constraint algebra are verified, the work supplies a concrete example of applying the deformed light-cone null-reduction technique to gauge theories, thereby extending its reach and revealing additional Carrollian models not previously obtained.

major comments (1)
  1. [Abstract] Abstract: the central claim that the chosen Bargmann-deformed light-cone background and scalings preserve the first-class nature of the U(1) Gauss constraint throughout the Carrollian limit is asserted without any displayed reduction ansatz, Poisson-bracket calculation, or verification that no second-class constraints arise. This verification is load-bearing for the construction and must be supplied explicitly (e.g., in the section deriving the reduced Hamiltonian and constraints).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed reading and for identifying the need to strengthen the presentation of the constraint analysis. We address the major comment below and will revise the manuscript to incorporate the requested explicit verification.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the chosen Bargmann-deformed light-cone background and scalings preserve the first-class nature of the U(1) Gauss constraint throughout the Carrollian limit is asserted without any displayed reduction ansatz, Poisson-bracket calculation, or verification that no second-class constraints arise. This verification is load-bearing for the construction and must be supplied explicitly (e.g., in the section deriving the reduced Hamiltonian and constraints).

    Authors: We agree that the explicit verification is essential for substantiating the central claim. The manuscript asserts preservation of the first-class Gauss constraint but does not display the full reduction ansatz, Poisson-bracket computations, or explicit check against second-class constraints. In the revised manuscript we will add these calculations in the section on the reduced Hamiltonian and constraints, including the ansatz for the fields and momenta, the computation of the relevant Poisson brackets, and the demonstration that the Gauss constraint remains first-class with no second-class constraints generated by the reduction. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper presents an explicit constructive procedure: Kaluza-Klein-like null reduction of a complex Maxwell field on a Bargmann-deformed light-cone background, with different scalings yielding magnetic/electric Carrollian theories while preserving the first-class U(1) Gauss constraint. No fitted parameters are renamed as predictions, no self-definitional loops appear in the reduction ansatz, and no load-bearing self-citations or uniqueness theorems imported from prior author work are invoked to force the result. The derivation chain is self-contained as a direct reduction from the higher-dimensional setup; the central claim (constraint preservation and theory diversity) follows from the stated procedure without reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central construction rests on the choice of a specific deformed background and scaling parameters whose validity is asserted but not derived from more fundamental principles in the abstract.

free parameters (1)
  • scaling parameters for magnetic vs electric limits
    Different scalings are chosen to obtain the magnetic or electric Carrollian theory; these are not derived but selected to match desired limits.
axioms (1)
  • domain assumption The Bargmann deformed light-cone background preserves the first-class U(1) Gauss constraint in the Carrollian limit.
    Invoked as the key property enabling manifest gauge symmetry throughout the reduction.

pith-pipeline@v0.9.1-grok · 5667 in / 1391 out tokens · 33104 ms · 2026-06-26T11:44:48.201210+00:00 · methodology

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Reference graph

Works this paper leans on

46 extracted references · 7 linked inside Pith

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    The kinetic terms must remain finite, and the Gauss-multiplier term should also survive to enforce the constraint

    Standard contraction For the magnetic contraction we wish to keep the mag- netic energy ∝ |F ′ ij|2 while suppressing the electric energy ∝ |Π′i|2. The kinetic terms must remain finite, and the Gauss-multiplier term should also survive to enforce the constraint. Examining Table I, a consistent choice of exponents is γA =−1, γ Π = 0, α A =−2, αΠ = 1, β A =...

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    If one wishes to avoid introducingm, a viable choice is γA =−1, γ Π = 0, α A =−2, αΠ = 1, β A =−1, β Π = 0, µ=−3

    Contraction induces decoupling with the scalar sector It should be noted that in (3.4), A− is no longer present, which of course stems from our choice of scaling exponents. If one wishes to avoid introducingm, a viable choice is γA =−1, γ Π = 0, α A =−2, αΠ = 1, β A =−1, β Π = 0, µ=−3. (3.14) And the action reads S(1) mag = Z dτ d⃗ x Πi∂τ Ai + Πτ ∂τ Aτ − ...

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    Standard contraction To preserve the electric energy ∝ ΠiΠi while discarding the magnetic energy, γA = 0, γ Π =−1, α A =−1, αΠ = 0, β A = 0, β Π = 0, µ=−2. (3.17) Thec→0 limit yields the real action: Selec = Z dτ d⃗ x h Πi∂τ Ai +(Πτ ∂τ Aτ) − 1 2ΠiΠi +A τ ∂iΠi −uΠ τ i . (3.18) Varying action (3.17) yields several equations of motion: •Variation with respec...

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    Contraction induces decoupling with the scalar sector If we choose the following scaling: γA = 0, γ Π =−1, α A =−1, αΠ = 0, β A = 0, β Π =−1, µ=−2, (3.26) we can preserve scalar sector A− but in a decoupled way: S(1) elec = Z dτ d⃗ x h Πi∂τ Ai + Πτ ∂τ Aτ + Π−∂τ A− −1 2ΠiΠi − 1 2Π−Π− +A τ ∂iΠi −uΠ τ i . (3.27) The new equations of motion are ∂τ A− = Π−, ∂ ...

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    Contraction induces coupling with the scalar sector We choose the following scaling: γA = 0, γ Π =−1, α A = 0, αΠ = 0, β A =−1, β Π = 0, µ= 0, (3.32) to obtain the action preserving scalar sector A− but in a coupled way: S(3) elec = Z dτ d⃗ x h Πi∂τ Ai + Π−∂τ A− − 1 2ΠiΠi −1 2(∂iA−)(∂iA−)−Π i∂iA− i . (3.33) The equations of motion are δΠi :∂ τ Ai = Πi +∂ ...

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