Geodesic
$\text{Spin}^c$-structures and Seiberg–Witten equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 245-250 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Seiberg–Witten equations, found at the end of the $20$th century, are one of the main discoveries in the topology and geometry of four-dimensional Riemannian manifolds. They are defined in terms of a $\text{Spin}^c$–structure that exists on any four-dimensional Riemannian manifold. Like the Yang–Mills equations, the Seiberg–Witten equations are the limit case of a more general supersymmetric Yang–Mills equations. However, unlike the conformally invariant Yang–Mills equations, the Seiberg–Witten equations are not scale invariant. Therefore, in order to obtain “useful information” from them, one must introduce a scale parameter $\lambda$ and pass to the limit as $\lambda\to\infty$. This is precisely the adiabatic limit studied in this paper.
Keywords: $\text{Spin}^c$-structures, Dirac operator, Seiberg–Witten equations
Mots-clés : adiabatic limit. 
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A. G. Sergeev. $\text{Spin}^c$-structures and Seiberg–Witten equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 245-250. http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a3/

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