The anomalous magnetic moment of the electron and the proton

Abstract

The Schwebel-Sachs self-consistent field theory of quantum electrodynamics is used to calculate the anomalous magnetic moment of the electron without recourse to renormalization and perturbation techniques. It was shown by the originators of the theory that their basic postulate, that the « laws of nature must be described in terms of field variables which may be associated only with elementary interactions », led to an elimination of the self-interactions that plagued classical theory and to a new electromagnetic interaction, the dual Lorentz interaction, which has the form ϱH−(1/c)(j×E). It is shown that this dual Lorentz interaction gives rise to an additional magnetic interaction which may be interpreted as the anomalous magnetic moment. The anomaly is found to beA=2mcg/ħ whereg is the coupling constant of of the field-current interaction representing the dual Lorentz interaction and has the dimension of length. Using the value ofg obtained from the Lamb shift calculations of a previous paper (1), it is shown thatA=1.087·10−3. The small discrepancy between this value and that of the free relativistic electron measurement is attributed to approximations made in the Lamb shift calculations. Recalculation ofg on the basis of the experimental value of the anomaly yieldsg=2.24·10−14 cm. Calculation of the proton anomaly givesA=2.14 compared to the magnetic resonance value of 1.79. It would be of interest and value to determine the magnetic moment of the proton under the same experimental conditions which determine the magnetic moment of the « free » electron.