  By analysing the work of Campolattaro we argue that the second Seiberg-Witten
equation over the Spin^c_4 manifold, i.e., F^+_{ij}=< M,S_ij M >, is the
generalization of the Campolattaro's description of the electromagnetic field
tensor F^{\mu\nu} in the bilinear form F^{\mu\nu}=\bar{\Psi} S^{\mu\nu}\Psi. 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 Spin^c_4 manifold.
