Noncommuting Gauge Fields as a Lagrange Fluid

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...

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Bibliographic Details
Published in:Annals of physics 2002-11, Vol.301 (2), p.157-173
Main Authors: Jackiw, R., Pi, S.-Y., Polychronakos, A.P.
Format: Article
Language:English
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Summary: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.
ISSN:0003-4916
1096-035X
DOI:10.1006/aphy.2002.6290