Lagrangian magnetic moment from polarization

An effective Lagrangian term for the electron magnetic moment, and more generally electromagnetic form factors, is calculated by considering the background field method. Two Fierz transformations are performed for a one-photon exchange interaction, and the ambiguity in doing such transformations is exploited. The resulting effective interaction may exhibit an approximated rotational chiral symmetry either for the scalar-pseudoscalar currents interaction or for the vector-axial currents interaction. The leading terms in the expansion of the fermion determinant yield the leading QED effective action with the complete one loop electromagnetic form factors. A model is proposed to produce the tree level magnetic moment term.