dorsal/arxiv
View SchemaThe locally-conserved current density of the Lienard-Wiechert field
| Authors | Andre Gsponer |
|---|---|
| Categories | |
| ArXiv ID | physics/0612090 |
| URL | https://arxiv.org/abs/physics/0612090 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
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.
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"abstract": "The complete charge-current density and field strength of an arbitrarily\naccelerated relativistic point-charge are explicitly calculated. That current\nincludes, apart from the well-established delta-function term which is\nsufficient for its global conservation, additional contributions depending on\nthe second and third proper-time derivatives of the position. These extra\ncontributions are necessary for the local conservation of that current, whose\ndivergence must vanish {identically} even if it is a distribution, as is the\ncase here. Similarly, the field strength includes an additional delta-like\ncontribution which is necessary for obtaining this result. Altogether, the\nLienard-Wiechert field and charge-current density must therefore be interpreted\nas nonlinear generalized functions, i.e., not just as distributions, even\nthough only linear operations are needed to verify local charge-current\nconservation.",
"arxiv_id": "physics/0612090",
"authors": [
"Andre Gsponer"
],
"categories": [
"physics.class-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "The locally-conserved current density of the Lienard-Wiechert field",
"url": "https://arxiv.org/abs/physics/0612090"
},
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"source": {
"execution_id": "874fd7fa-e8cc-404e-b9fb-28d069f847c5",
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"variant": "snapshot-2026-03-01",
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