U(1) Connection, Nonlinear Dirac-like Equations and Seiberg-Witten Equations

Details U(1) Connection, Nonlinear Dirac-like Equations and Seiberg-Witten Equations U(1) Connection, Nonlinear Dirac-like Equations and Seiberg-Witten Equations

2000-01-22

arxiv.org/abs/hep-th/0001147v1

Int.J.Theor.Phys. 37 (1998) 2115-2125

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

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.

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