Seiberg-Witten Equations on Pseudo-Riemannian Spin(c) Manifolds With Neutral Signature

DEĞİRMENCİ N., Karapazar S.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.20, sa.1, ss.73-88, 2012 (SCI-Expanded) identifier

  • 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.