A Phenomenological Theory of the Lamb Shift and of Anomalous Magnetic Moments

Publisher Website
Google Scholar
Abstract
If one assumes that self-interactions don't exist and can be ignored, the explanation of the anomalous magnetic moments of proton and electron and the Lamb shift require new types of interaction between protons, photons, and electrons. A theory with such additional interactions is here developed in gauge-independent form, thus avoiding longitudinal and scalar photons throughout. The covariance of the formalism is proved. The resulting modification of Maxwell's equations for charged elementary particles in the vacuum involves only the introduction of an intrinsic polarization and magnetization of elementary particles, so that these equations for the vacuum now take the familiar form of the macroscopic Maxwell equations in matter. A further modification of the Dirac equation for electrons and protons involves the introduction of a delta-function interaction between them, opposite in sign to the Coulomb interaction. It is indicated how one can derive an energy density tensor for this theory. It is then shown how this formalism explains the anomalous moments and the Lamb shift. The three new interaction constants are adjusted to the experimental data. The dependence of the Lamb shift on the quantum numbers automatically comes out to be nearly the same and the dependence on the atomic number to be exactly the same as in the theory of Bethe, French and Weisskopf.