The anomalous magnetic moment of the electron, , is computed using dispersion theory. The analytic continuation is made in the mass of one of the external electron lines and only the one-electron one-photon states are retained in the absorptive amplitude. In this way we relate to the Compton amplitude which has a known exact threshold behavior. Our approximation is an expansion in the low-energy behavior rather than a perturbation expansion in powers of 1/137, and we are able to show that a major contribution to comes from the low-mass region of the electron-photon system near the threshold of the absorptive amplitude. First, in a purely nonrelativistic calculation, we find that a major part of the correction is accounted for by the Thomson limit. Further refining our calculation by including the exact residue of the pole terms in the Compton amplitude in accord with the low-energy theorem on Compton scattering, we find that electron-photon states below in the absorptive amplitude reproduce 90% of the contribution and predict a value of for the sixth-order term. We also give a simple physical interpretation of the difference of the muon and electron values. Finally we calculate with this approach the anomalous magnetic moments of the proton and neutron, with the Kroll-Ruderman theorem on meson photoproduction providing the low-energy "anchor" in this case. Again retaining only the low-mass region of the absorptive amplitude, we obtain fair agreement with the magnitude and the isovector character of the moments, finding and .
- Received 14 June 1965
©1965 American Physical Society