Seiberg-Witten Equations on Pseudo-Riemannian Spin(c) Manifolds With Neutral Signature
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.20, sa.1, ss.73-88, 2012 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 20 Sayı: 1
- Basım Tarihi: 2012
- Dergi Adı: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.73-88
- Anahtar Kelimeler: Neutral metric, Pseudo-Riemannian spine(c)-structure, Dirac operator, Seiberg-Witten equations
- Anadolu Üniversitesi Adresli: Evet
Özet
Pseudo-Riemannian spin(c) 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 spin(c) 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 flat space.