# Geometric Symmetries in Superfluid Vortex Dynamics

Source: [Geometric Symmetries in Superfluid Vortex Dynamics](<https://www.sota2.com/research/paper/68fa2f631e209131ce86b639>)

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

Data updated: 2025-10-24T17:30:52.117Z

Authors: Evgeny Kozik, Boris Svistunov

Published: 2010-06-02T21:44:36.000Z

## Abstract

Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, $w(z)=x(z)+iy(z)$, describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which---apart from their rather specific expressions in terms of $w(z)$---are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines---the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wavenumber space. Similar considerations apply to other systems with purely geometric degrees of freedom.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1006.0506>)

[PDF](<https://arxiv.org/pdf/1006.0506.pdf>)