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Seiberg-Witten Equations on Pseudo-Riemannian Spinc Manifolds With Neutral Signature

Published Online: 17 May 2013
Page range: 73 - 88
Journal Details
License
Format
Journal
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English
Copyright
© 2020 Sciendo
Abstract

Pseudo-Riemannian spinc manifolds were introduced by Ikemakhen in [7]. In the present work we consider pseudo-Riemannian 4-manifolds with neutral signature whose structure groups are SO+(2; 2). We prove that such manifolds have pseudo-Riemannian spinc structure. We construct spinor bundle S and half-spinor bundles S+ and S- on these manifolds. For the first Seiberg-Witten equation we define Dirac operator on these bundles. Due to the neutral metric self-duality of a 2-form is meaningful and it enables us to write down second Seiberg-Witten equation. Lastly we write down the explicit forms of these equations on 4-dimensional at space

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