On the electrodynamics of spinning particles

We consider the electrodynamics of spinning point particles. We introduce a modification of the Lorentz force law which can be interpreted as a classical limit of the Dirac-Klein-Gordon equation. An improved version of the inhomogeneous Maxwell equations is constructed for the description of the classical fields of spinning particles. Both classical and quantum electrodynamics are shown to predict relativistic time-dilation effects for spinning particles in an electromagnetic field, even in the limit of zero velocity. The life-time of unstable charged particles moving in a Coulomb field is computed for both spin-0 and spin-12 particles. Comparison shows (relatively small) spin effects to be present. The magnitude of further spin-dependent corrections from hyperfine interactions is computed. A measurement of the life-time of muons in atomic bound states separated by such spin-dependent hyperfine interactions would provide a clean test for the effect we predict. Similar effects are shown to arise in non-abelian gauge theories such as QCD.