2006/12/10 by Andre Gsponer, Gsponer, Andre · 1 citation
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #physics.class-ph
paper · pdf · doi:10.48550/arxiv.physics/0612090
9 pages. Short version of arXiv:physics/0612232
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. That current 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. These extra contributions are necessary for the local conservation of that current, whose divergence must vanish identically even if it is a distribution, as is the case here. Similarly, the field strength includes an additional delta-like contribution which is necessary for obtaining this result. Altogether, 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 needed to verify local charge-current conservation.