  A fully relativistically covariant formulation of the classical Maxwell
electrodynamics of an arbitrarily-moving point charge is presented, purely in
terms of gauge invariant potentials without entailing any gauge fixing. A new,
relativistically covariant energy-momentum tensor for the radiation fields is
derived and yields results for the angular power distribution, in full
agreement with results derived in a frame-dependent manner in standard texts of
classical electrodynamics. This is then used to present a full derivation, not
available in standard texts, of the energy-momentum and orbital angular
momentum of a relativistic point charge. Radiation backreaction is turned on
and the system reanalyzed Lorentz-covariantly, including effects of mass
renormalization. This leads us to reiterate earlier conclusions regarding the
inherent inadequacy of classical Maxwell electrodynamics. The Abraham-Lorentz
equation is derived en passant in appropriate limits without requiring any
extraneous structural artifact, and the Landau-Lifschitz proposal for
modification of the theory is also critically reviewed.
