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We review the connection between noncommutative gauge theory, matrix models and fluid mechanical systems.
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A. P. Polychronakos, “Integrable systems from gauged matrix models,” Phys. Lett. B 266
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A. H. Chamseddine and J. Frohlich, “The Chern-Simons action in noncommutative geometry,” J. Math. Phys. 35
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A. P. Polychronakos, “Waves and solitons in the continuum limit of the Calogero-Sutherland model,” Phys. Rev. Lett. 74
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B. Sakita, “Collective variables of fermions and bosonization,” Phys. Lett. B 387
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A. Connes, M. R. Douglas and A. S. Schwarz, “Noncommutative geometry and matrix theory: Compactification on tori,” JHEP 9802
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V. Arnold and B. Khesin, “Topological Methods in Hydrodynamics” (Springer, Berlin, 1998)
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N. Seiberg and E. Witten, “String theory and noncommutative geometry,” JHEP 9909
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J. Goldstone, unpublished communication to R. Jackiw; D. B. Fairlie and C. K. Zachos, “Infinite Dimensional Algebras, Sine Brackets and SU(Infinity),” Phys. Lett. B 224
D. Bak, K. M. Lee and J. H. Park, “Comments on noncommutative gauge theories,” Phys. Lett. B 501
2001
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H. Liu, “*-Trek II: *n operations, open Wilson lines and the Seiberg-Witten map,” Nucl. Phys. B 614
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Y. Okawa and H. Ooguri, “An exact solution to Seiberg-Witten equation of noncommutative gauge theory,” Phys. Rev. D 64
2001
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A. P. Polychronakos, “Quantum Hall states as matrix Chern-Simons theory,” JHEP 0104
2001
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S. Hellerman and M. Van Raamsdonk, “Quantum Hall physics equals noncommutative field theory,” JHEP 0110
2001
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C. Duval and P. A. Horvathy, “Exotic Galilean symmetry in the non-commutative plane, and the Hall effect,” J. Phys. A 34
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1999
Cited alongside, same era.
J. Madore, S. Schraml, P. Schupp and J. Wess, ‘Gauge theory on noncommutative spaces,” Eur. Phys. J. C 16
2000
Cited alongside, same era.
U. Carow-Watamura and S. Watamura, “Differential calculus on fuzzy sphere and scalar field,” Int. J. Mod. Phys. A 13
2000
Cited alongside, same era.
A. P. Polychronakos, “Flux tube solutions in noncommutative gauge theories,” Phys. Lett. B 495
2000
Cited alongside, same era.
D. J. Gross, A. Hashimoto and N. Itzhaki, “Observables of non-commutative gauge theories,” Adv. Theor. Math. Phys. 4
2000
Cited alongside, same era.
A. P. Polychronakos, “Noncommutative Chern-Simons terms and the noncommutative vacuum,” JHEP 0011
2000
Cited alongside, same era.
S. Deser, R. Jackiw and S. Templeton, “Topologically massive gauge theories,” Annals Phys. 140
2000
Cited alongside, same era.
2001
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Z. Guralnik, R. Jackiw, S. Y. Pi and A. P. Polychronakos, “Testing non-commutative QED, constructing non-commutative MHD,” Phys. Lett. B 517
2001
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C K. Zachos, “Deformation quantization: Quantum mechanics lives and works in phase space,” Int. J. Mod. Phys. A 17
2002
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G. H. Chen and Y. S. Wu, “One-loop shift in noncommutative Chern-Simons coupling,” Nucl. Phys. B 593
2002
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R. Jackiw, S. Y. Pi and A. P. Polychronakos, “Noncommuting gauge fields as a Lagrange fluid,” Annals Phys. 301
2002
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A. P. Polychronakos, “Seiberg-Witten map and topology,” Annals Phys. 301
2002
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J. H. Brodie, L. Susskind and N. Toumbas, “How Bob Laughlin tamed the giant graviton from Taub-NUT space,” JHEP 0102
2002
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D. Karabali and B. Sakita, “Chern-Simons matrix model: Coherent states and relation to Laughlin wavefunctions,” Phys. Rev. B 64
2002
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R. J. Szabo, “Quantum field theory on noncommutative spaces,” Phys. Rept. 378
2003
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T. H. Hansson, J. Kailasvuori and A. Karlhede, “Charge and current in the quantum Hall matrix model,” Phys. Rev. B 68
2003
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R. Jackiw, V. P. Nair, S. Y. Pi and A. P. Polychronakos, “Perfect fluid theory and its extensions,” J. Phys. A 37
2004
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B. Morariu and A. P. Polychronakos, “Finite noncommutative Chern-Simons with a Wilson line and the quantum Hall effect,” JHEP 0107
2005
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D. Berenstein, “A matrix model for a quantum Hall droplet with manifest particle-hole symmetry,” Phys. Rev. D 71
2005
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D. Karabali and V. P. Nair, “Quantum Hall effect in higher dimensions,” Nucl. Phys. B 641
2005
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A. P. Polychronakos, “Chiral actions from phase space (quantum Hall) droplets,” Nucl. Phys. B 705
2005
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W. Bietenholz, F. Hofheinz and J. Nishimura, “Numerical results on the non-commutative lambda Phi**4 model,” Nucl. Phys. Proc. Suppl. 129
2006
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For reviews of the Calogero model closest in spirit to the present discussion see A. P. Polychronakos, “Generalized statistics in one dimension,” published in ‘Topological aspects of low-dimensional systems,’ Les Houches Session LXIX (1998), Springer Ed. [hep-th/9902157]; “Physics and mathematics of Calogero particles,” J. Phys. A 39
2006
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A. P. Polychronakos, “Bosonization in higher dimensions via noncommutative field theory,” Phys. Rev. Lett. 96
2006
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