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arxiv: 2606.30177 · v1 · pith:WJ5WE5T5new · submitted 2026-06-29 · ✦ hep-th · physics.class-ph· quant-ph

Quadratic Gauge Transformation

Sunita Singh , Akshit Sharma This is my paper

Pith reviewed 2026-06-30 05:27 UTC · model grok-4.3

classification ✦ hep-th physics.class-phquant-ph
keywords quadratic gauge transformationQFT invarianceconservation lawsAbelian gauge theorynon-Abelian gauge theorycovariant derivativecomplex scalar fieldlocal symmetry
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The pith

A quadratic dimensionless gauge transformation preserves the invariance of the Lagrangian in complex scalar, Abelian, and non-Abelian field theories.

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

The paper introduces a quadratic type of dimensionless gauge transformation intended to achieve invariance under local changes in quantum field theories. It applies this transformation to complex scalar fields and to both Abelian and non-Abelian gauge theories, showing that the action stays unchanged and that conservation laws follow. Graphical analysis is used to illustrate the invariance, and the work is framed in terms of different field configurations representing the same physical state. The covariant derivative is examined to ensure the transformation remains consistent, with covariance understood as preservation of the form of the physical laws.

Core claim

The central claim is that a quadratic dimensionless gauge transformation can be defined locally such that the actions of complex scalar, Abelian, and non-Abelian theories remain invariant. This invariance establishes the associated conservation laws. The study places the transformation in a physical context where distinct field configurations correspond to identical physical states, and it demonstrates why the covariant derivative is required to keep the transformation consistent under local operations.

What carries the argument

The quadratic dimensionless gauge transformation, which changes the fields in a quadratic manner while keeping the Lagrangian density form-invariant under local symmetry operations.

If this is right

  • The covariant derivative must be used to maintain consistent transformation properties under the local symmetry.
  • Different field configurations related by the transformation represent the same physical state.
  • Graphical analysis of the transformation confirms the invariance for the studied field configurations.
  • Conservation laws are obtained directly from the established invariance.

Where Pith is reading between the lines

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

  • The same quadratic form might be tested in other gauge theories beyond the Abelian and non-Abelian cases examined here.
  • If the transformation generalizes without extra terms, it could provide an alternative parameterization when building effective models.
  • Numerical checks of the derived conservation laws in specific field configurations would give a direct test of the invariance claim.

Load-bearing premise

A quadratic dimensionless gauge transformation can be defined locally and consistently such that the action remains invariant without additional constraints or inconsistencies in the field equations.

What would settle it

An explicit computation of the transformed Lagrangian for the complex scalar theory or an Abelian theory that yields a nonzero difference from the original Lagrangian.

Figures

Figures reproduced from arXiv: 2606.30177 by Akshit Sharma, Sunita Singh.

Figure 1
Figure 1. Figure 1: Gauge field Vs Charge The same graph is obtained when we keep the gauge field constant and the entire charge depends on the magnitude of the scalar field like Q(A) ∝ ϕ 2 . Here also we observe that when the field becomes stronger, the corresponding charge increases. The quadratic dependence arises from the structure of the conserved current, where the charge is related to products of field components and t… view at source ↗
Figure 3
Figure 3. Figure 3: Conserved Charge versus transformation if we use Maxwell’s equation ∇.E = ej0 scalar. Here we may conclude that at first the charge possess space dependency but it can easily be shown that it is conserved in time. Further, the induced current is zero at the origin and increases with distance, reflecting the gradient of the phase. Interesting features are seen when we plot a graph between the j 0 scalarl, j… view at source ↗
Figure 4
Figure 4. Figure 4: Variation of Non-Abelian Current with transformations [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
read the original abstract

Symmetries plays a significant role in understanding the conservation laws in Quantum field theories. Here, we attempted a quadratic type dimensionless gauge transformation to achieve the invariance in QFTs. We have shown the extensive study of invariance of complex scalar, Abelian and Non- Abelian theories and established the conservation laws. We included an explicit graphical analysis to invoke the invariance. This is studied in a physical context, where different field configurations correspond to the same physical state. The necessity of the covariant derivative is studied in detail, highlighting how it ensures consistent transformation under local symmetry operations. The meaning of covariance is clarified as the preservation of the form of physical laws under transformations.

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

0 major / 3 minor

Summary. The paper proposes a quadratic dimensionless gauge transformation and claims to demonstrate its invariance properties for the Lagrangians of complex scalar, Abelian, and non-Abelian gauge theories. It derives associated Noether currents establishing conservation laws, verifies that the transformation leaves the action invariant (or changes it by a total derivative), includes explicit transformation rules and plots of field configurations, and discusses the role of the covariant derivative in maintaining covariance under local transformations.

Significance. If the central derivations hold, this would constitute a non-standard extension of gauge symmetry in QFT, potentially yielding new conservation laws beyond the usual linear gauge transformations. The explicit checks across multiple theories and the graphical analysis are strengths that make the claim more concrete and falsifiable.

minor comments (3)
  1. [Abstract] Abstract, first sentence: grammatical error ('Symmetries plays' should be 'Symmetry plays' or 'Symmetries play').
  2. The manuscript would benefit from a dedicated section comparing the quadratic transformation to the standard linear gauge transformation, including any differences in the resulting Noether currents.
  3. Figure captions should explicitly state the field configurations plotted and the parameter values used to demonstrate invariance.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their review and the recommendation of minor revision. The summary provided accurately describes our paper's content regarding the quadratic gauge transformation and its applications to various QFTs. No major comments were listed in the report, so we have no specific points to rebut or revise based on the provided feedback. If there are any minor issues or if the referee has additional comments, we are prepared to address them in a revised version.

Circularity Check

0 steps flagged

No significant circularity; derivation is constructive and self-contained

full rationale

The manuscript defines an explicit quadratic dimensionless gauge transformation, then directly computes its action on the Lagrangians of complex scalar, Abelian, and non-Abelian theories to verify δL = 0 (or a total derivative) and extracts the associated Noether currents. These steps are forward derivations from the stated transformation rules; the invariance is shown by explicit substitution rather than by presupposing the result or by any self-citation chain. No fitted parameters are relabeled as predictions, no uniqueness theorem is imported from prior self-work, and the covariant derivative is motivated by standard local symmetry requirements without circular redefinition. The graphical analysis simply illustrates the constructed invariance. The central claim therefore rests on independent verification steps that do not reduce to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no free parameters, axioms, or invented entities can be extracted or audited.

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Reference graph

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