The Dirac bispinor form of Maxwell’s equations and the anomalous hyperfine structure of relativistic hydrogen

Abstract

We show that, in addition to the usual covariant tensor form of Maxwell’s equations, a more general, manifestly covariant, Dirac bispinor form of them exists. A study of the Lagrangian formulation of electrodynamics, utilizing this more general bispinor electromagnetic-field structure, is conducted. We find that, in addition to the conventional Lorentz force interaction, a new electromagnetic « spinor-torque » interaction, related to the bispinor structure, is generated. We study the effect that Dirac bispinor electrodynamics has on the spectrum of relativistic hydrogen and show that the new « spinor-torque » interaction will contribute an extra anomalous hyperfine structure term, in addition to that generated by proton spin structure and quantum electrodynamic effects. Estimates of the value of the coupling constant associated with the « spinor-torque » interaction, which has the dimensions of a length, are given.