Geodesic
Nontrivial Solutions of Seiberg--Witten Equations on the Noncommutative 4-Dimensional Euclidean Space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear dynamics, Tome 251 (2005), pp. 127-138.

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Noncommutative Seiberg–Witten equations on the noncommutative Euclidean space $\mathbb R^4_\theta$ are studied that are obtained from the standard Seiberg–Witten equations on $\mathbb R^4$ by replacing the usual product with the deformed Moyal $\star$-product. Nontrivial solutions of these noncommutative Seiberg–Witten equations are constructed that do not reduce to solutions of the standard Seiberg–Witten equations on $\mathbb R^4$ for $\theta \to 0$. Such solutions of the noncommutative equations on $\mathbb R^4_\theta$ exist even when the corresponding commutative Seiberg–Witten equations on $\mathbb R^4$ do not have any nontrivial solutions. 
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     title = {Nontrivial {Solutions} of {Seiberg--Witten} {Equations} on the {Noncommutative} {4-Dimensional} {Euclidean} {Space}},
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M. Wolf; A. D. Popov; A. G. Sergeev. Nontrivial Solutions of Seiberg--Witten Equations on the Noncommutative 4-Dimensional Euclidean Space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear dynamics, Tome 251 (2005), pp. 127-138. http://geodesic.mathdoc.fr/item/TM_2005_251_a4/

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