Noncommuting Gauge Fields as a Lagrange Fluid

TL;DR

This paper explores the connection between fluid mechanics and noncommuting gauge fields, introducing gauge-covariant transformations and relating the Seiberg-Witten map to fluid dynamics mappings.

Contribution

It establishes a novel link between Lagrangian fluid descriptions and noncommuting gauge theories, providing a new perspective on gauge transformations and variable mappings.

Findings

Identifies gauge potentials and Poisson structures as classical precursors in fluid mechanics.

Constructs gauge-covariant coordinate transformations on noncommutative spaces.

Relates the Seiberg-Witten map to the Lagrange-Euler map in fluid dynamics.

Abstract

The Lagrange description of an ideal fluid gives rise in a natural way to a gauge potential and a Poisson structure that are classical precursors of analogous noncommuting entities. With this observation we are led to construct gauge-covariant coordinate transformations on a noncommuting space. Also we recognize the Seiberg-Witten map from noncommuting to commuting variables as the quantum correspondent of the Lagrange to Euler map in fluid mechanics.