  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.
