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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
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