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It is shown how Seiberg-Witten equations can be obtained by means of Fedosov deformation quantization of endomorphism bundle and the corresponding theory of equivalences of star products.
B.V. Fedosov, A simple geometrical construction of deformation quantization, J. Diff. Geom. 40
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C. Emmrich and A. Weinstein, The differential geometry of Fedosov’s quantization, in Lie Theory and Geometry. In Honor of Bertram Kostant eds. J.-L. Brylinski, R. Brylinski, V. Guillemin and V. Kac (Birkhäuser, 1994), hep-th/9311094
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I. Gelfand, V. Retakh and M. Shubin, Fedosov Manifolds, Adv. Math. 136
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N. Seiberg and E. Witten, String theory and noncommutative geometry, J. High Energy Phys. 09
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S. Goto and H. Hata, Noncommutative monopole at the second order in θ \theta , Phys. Rev. D 62
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B. Jurčo and P. Schupp, Noncommutative Yang-Mills from equivalence of star products, Eur. Phys. J. C 14
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B. Jurčo, L. Möller S. Schraml, P. Schupp and J. Wess, Construction of non-abelian gauge theories on noncommutative spaces, Eur. Phys. J. C 21
2001
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D. M. Brace, B. L. Cerchiai, A. F. Pasqua, U. Varadarajan and B. Zumino, A cohomological approach to the non-abelian Seiberg-Witten map, J. High Energy Phys. 06
2001
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B. Jurčo, P. Schupp and J. Wess, Nonabelian noncommutative gauge theory via noncommutative extra dimensions, Nucl. Phys. B 604
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P. Kraus and M. Shigemori, Non-commutative instantons and the Seiberg-Witten map, J. High Energy Phys. 06
2002
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M. Gadella, M. A. del Olmo and J. Tosiek, Geometrical origin of the *-product in the Fedosov formalism, J. Geom. Phys. 55
2005
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P. Bieliavsky, M. Cahen, S. Gutt, J. Rawnsley and L. Schwachhöfer, Symplectic connections, Int. J. Geom. Meth. Mod. Phys. 3
2006
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P. Schupp, Noncommutative field theory, Fortschr. Phys. 54
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2007
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J. Trampetić and M. Wohlgenannt, Remarks on the second-order Seiberg-Witten maps, Phys. Rev. D 76
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M. Gadella, M. A. del Olmo, J. Tosiek, Quantization on a 2-dimensional phase space with a constant curvature tensor, Annals Phys. 307
2003
Cited alongside, same era.
L. Möller, Second order expansion of action functionals of noncommutative gauge theories, J. High Energy Phys. 10
2004
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2008
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