  A basic leapfrog integrator and its energy-preserving and variational /
symplectic variants are proposed and studied for the numerical integration of
the equations of motion of relativistic charged particles in an electromagnetic
field. The methods are based on a four-dimensional formulation of the equations
of motion. Structure-preserving properties of the numerical methods are
analysed, in particular conservation and long-time near-conservation of energy
and mass shell as well as preservation of volume in phase space. In the
non-relativistic limit, the considered methods reduce to the Boris algorithm
for non-relativistic charged-particle dynamics and its energy-preserving and
variational / symplectic variants.
