. cl as s - ph ] 2 9 Ja n 20 07 Derivation of the potential , field , and locally - conserved charge - current density of an arbitrarily moving point - charge

The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. The current density includes, apart from the well-established delta-function term which is sufficient for its global conservation, additional contributions depending on the second and third proper-time derivatives of the position, which are necessary for its local conservation as required by the internal consistency of classical electrodynamics. Similarly, the field strength includes an additional delta-like contribution which is necessary for obtaining this result. The four-potential from which this field and the conserved charge-current density derive is found to be unique in the sense that it is the only one reducing to an invariant scalar function in the instantaneous rest frame of the point-charge that leads to a point-like locally-conserved charge-current density. PACS numbers: 03.50.De Classical electromagnetism, Maxwell equations