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

Abstract

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 $\ensuremath{\Delta}$-functions which describe the interaction of virtual electrons and photons with the vacuum are given to order $\ensuremath{\alpha}$. The addition to the magnetic moment to order ${\ensuremath{\alpha}}^{2}$ is found to be finite after the charge of the electron is renormalized consistently. This correction amounts to $\frac{\ensuremath{-}2.97{\ensuremath{\alpha}}^{2}}{{\ensuremath{\pi}}^{2}}$ Bohr magneton so that the magnetic moment of the electron is $\ensuremath{\mu}=1.001147$ Bohr magnetons.