Splitting of the Maxwell Tensor: Radiation Reaction without Advanced Fields

It is shown that, for a classical point charge, the "bound" electromagnetic four-momentum contains, besides the generally accepted "Coulomb mass"\ifmmode\times\else\texttimes\fi{}four-velocity term, the extra term $\ensuremath{-}\frac{2}{3}{e}^{2}{a}^{\ensuremath{\mu}}$. This is accomplished by exploiting some interesting properties of the usual separation of the retarded field of a moving charge into a velocity and an acceleration part (both retarded). In this way a new derivation of the Lorentz-Dirac equation of motion emerges. In particular, in the light of such a derivation, the physical meaning of the "Schott term" is fully elucidated. The asymptotic condition of uniform motion in the remote past is seen to be essential for the establishment of the differential equation of motion. In contrast with previous discussions, no advanced field need be introduced in any step of the work. Electromagnetic radiation is treated with no single use of asymptotic procedures. Further physical insight is obtained into Rohrlich's criterion for radiation.