Effect of the Anomalous Magnetic Moment of the Electron on the Nonlinear Lagrangian of the Electromagnetic Field

When the anomalous magnetic moment of the electron ($g\ne 2$) is considered, by adding a phenomenological Pauli term to the Dirac Hamiltonian, the exact solutions to the Dirac equation can still be found. Using these solutions, and the methods of Heisenberg and Euler and of Weisskopf, we derive, in addition to the usual nonlinear term, a new nonlinear term which is correct to relative order ${\alpha }^2$.