Noncommuting Gauge Fields as a Lagrange Fluid
arXiv:hep-th/0206014 · doi:10.1006/aphy.2002.6290
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.
19 pages; final version to appear in Annals of Physics