Surprising Symmetries in Relativistic Charge Dynamics

The eigenspinor approach uses the classical amplitude of the algebraic Lorentz rotation connecting the lab and rest frames to study the relativistic motion of particles. It suggests a simple covariant extension of the common definition of the electric field: the electromagnetic field can be defined as the proper spacetime rotation rate it induces in the particle frame times its mass-to-charge ratio. When applied to the dynamics of a point charge in an external electromagnetic field, the eigenspinor approach reveals surprising symmetries, particularly the invariance of some field properties in the rest frame of the accelerating charge. The symmetries facilitate the discovery of analytic solutions of the charge motion and are simply explained in terms of the geometry of spacetime. Symmetries of the uniformly accelerated charge and electric dipole are also briefly discussed.