Wolf, M.; Popov, A. D.; Sergeev, A. G. Nontrivial solutions of Seiberg-Witten equations on the noncommutative 4-dimensional Euclidean space. (English. Russian original) Zbl 1138.81524 Proc. Steklov Inst. Math. 251, 121-131 (2005); translation from Tr. Mat. Inst. Steklova 251, 127-138 (2005). Summary: 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.For the entire collection see [Zbl 1116.34001]. MSC: 81T75 Noncommutative geometry methods in quantum field theory 58B34 Noncommutative geometry (à la Connes) 81R60 Noncommutative geometry in quantum theory PDFBibTeX XMLCite \textit{M. Wolf} et al., in: Nonlinear dynamics. Collected papers. Transl. from the Russian. Moscow: Maik Nauka. 121--131 (2005; Zbl 1138.81524); translation from Tr. Mat. Inst. Steklova 251, 127--138 (2005) Full Text: MNR