Radiation reaction reexamined: bound momentum and Schott term

We review and compare two different approaches to radiation reaction in classical electrodynamics of point charges: a local calculation of the self-force using the charge equation of motion and a global calculation consisting in integration of the electromagnetic energy-momentum flux through a hypersurface encircling the world-line. Both approaches are complementary and, being combined together, give rise to an identity relating the locally and globally computed forces. From this identity it follows that the Schott terms in the Abraham force should arise from the bound field momentum and can not be introduced by hand as an additional term in the mechanical momentum of an accelerated charge. This is in perfect agreement with the results of Dirac and Teitelboim, but disagrees with the recent calculation of the bound momentum in the retarded coordinates. We perform an independent calculation of the bound electromagnetic momentum and verify explicitly that the Schott term is the derivative of the finite part of the bound momentum indeed. The failure to obtain the same result using the method of retarded coordinates tentatively lies in an inappropriate choice of the integration surface. We also discuss the definition of the delta-function on the semi-axis involved in the local calculation of the radiation reaction force and demonstrate inconsistency of one recent proposal.