Seiberg-Witten Equations on Four-Dimensional Lorentzian Spin(C) Manifolds

Abstract

New kind of spinors are introduced on four-dimensional Lorentzian Spin(c) manifolds in [1]. We define Dirac operator on such spinors. In [2] Seiberg-Witten-like equations are written down on Minkowski space. In the present work we generalize these equations to four-dimensional Lorentzian Spin(c)-manifolds.