Fourth-Order Corrections in Quantum Electrodynamics and the Magnetic Moment of the Electron

The covariant $S$ matrix formalism of Dyson has been applied to the calculation of the fourth-order radiative correction to the magnetic moment of the electron. Intermediate results for the covariant $\Delta$-functions which describe the interaction of virtual electrons and photons with the vacuum are given to order $\alpha$. The addition to the magnetic moment to order ${\alpha }^2$ is found to be finite after the charge of the electron is renormalized consistently. This correction amounts to $\frac{-2.97\mathrm{}{\alpha }^2}{{\pi }^2}$ Bohr magneton so that the magnetic moment of the electron is $\mu =1.001147\mathrm{}$ Bohr magnetons.