The magnetic moment of the electron

Abstract The spin magnetic dipole moment of the electron is computed to fourth order in perturbation theory. The procedure is to consider a system of one electron moving in a constant external magnetic field. The Green's function and mass operator for the electron are computed as functions of this field. The expectation value of the mass operator is the self-energy of the electron and the magnetic moment is identified from that part of the self-energy linear in the external field. The techniques used are illustrated in a calculation of the second-order moment. The derivation of the fourth-order moment is sketched. It is found to be μ(4) = −0.328 ( (α π) 2 in Bohr magnetons, where α is the fine-structure constant. This differs from the result of a previous calculation.