Seiberg-Witten equations on pseudo-Riemannian spinc manifolds with neutral signature
Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, vol.20, no.1, pp.73-89, 2012 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 20 Issue: 1
- Publication Date: 2012
- Doi Number: 10.2478/v10309-012-0006-7
- Journal Name: Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.73-89
- Keywords: Dirac operator, Neutral metric, Pseudo-Riemannian spinc-structure, Seiberg-Witten equations
- Open Archive Collection: AVESIS Open Access Collection
- Anadolu University Affiliated: Yes
Abstract
Pseudo-Riemannian spinc manifolds were introduced by Ikemakhen in [7]. In the present work we consider pseudoRiemannian 4-manifolds with neutral signature whose structure groups are SO+(2; 2). We prove that such manifolds have pseudoRiemannian spinc structure. We construct spinor bundle S and half-spinor bundles S+ and S-on these manifolds. For therst 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.