# Comment on "Symmetries and Interaction Coefficients of Kelvin waves" \[arXiv:1005.4575\] by Lebedev and L'vov

Source: [Comment on "Symmetries and Interaction Coefficients of Kelvin waves" \[arXiv:1005.4575\] by Lebedev and L'vov](<https://www.sota2.com/research/paper/68fa2f651e209131ce86bb18>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T17:31:54.873Z

Authors: Evgeny Kozik, Boris Svistunov

Published: 2010-06-09T12:46:22.000Z

## Abstract

We comment on the claim by Lebedev and L'vov \[arXiv:1005.4575\] that the symmetry with respect to a tilt of a quantized vortex line does not yet prohibit coupling between Kelvin waves and the large-scale slope of the line. Ironically, the counterexample of an effective scattering vertex in the local induction approximation (LIA) attempted by Lebedev and L'vov invalidates their logic all by itself being a notoriously known example of how symmetries impose stringent constraints on kelvon kinetics---not only the coupling in question but the kinetics in general are absent within LIA. We further explain that the mistake arises from confusing symmetry properties of a specific mathematical representation in terms of the canonical vortex position field w(z) = x(z) + iy(z), which explicitly breaks the tilt symmetry due to an arbitrary choice of the z-axis, with those of the real physical system recovered in final expressions.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1006.1789>)

[PDF](<https://arxiv.org/pdf/1006.1789.pdf>)