2006/12/23 by André Gsponer, Andre Gsponer, Gsponer, Andre · 2 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Engineering and Technology Innovations #Geophysical and Geoelectrical Methods #Quantum and Classical Electrodynamics #physics.class-ph
paper · pdf · doi:10.48550/arxiv.physics/0612232
25 pages. Long version of arXiv:physics/0612090
arxiv created 2008/12/31 · arxiv updated 2009/12/01
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 three-dimensional delta-function which is sufficient for its global conservation, additional delta-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 which implies that local charge-conservation is an identity. Similarly, the field strength includes an additional delta-contribution which is necessary for obtaining this result. The Lienard-Wiechert field and charge-current density must therefore be interpreted as nonlinear generalized functions, i.e., not just as distributions, even though only linear operations are necessary to verify charge-current conservation. 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.