Nonlinear Dirac-like Equations and Seiberg-Witten Equations

By analysing the work of Campolattaro we argue that the second SeibergWitten equation over the Spinc4 manifold, i.e., F + ij = 〈M,SijM〉, is the generalization of the Campolattaro’s description of the electromagnetic field tensor F in the bilinear form F = ΨSΨ. It turns out that the Seiberg-Witten equations (also the perturbed Seiberg-Witten equations) can be well understood from this point of view. We suggest that the second Seiberg-Witten equation can be replaced by a nonlinear Dirac-like Equation. We also derive the spinor representation of the connection on the associated unitary line bundle over the Spinc4 manifold.