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2009

A Rigorous Derivation of Electromagnetic Self-force

Gralla, Samuel E., Harte, Abraham I., Wald, Robert M.

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During the past century, there has been considerable discussion and analysis of the motion of a point charge, taking into account "self-force" effects due to the particle's own electromagnetic field.

We analyze the issue of "particle motion" in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density $J^a(\lambda)$ and stress-energy tensor $T_{ab} (\lambda)$ scale to zero size in an asymptotically self-similar manner about a worldline $\gamma$ as $\lambda \to 0$.
In this limit, the charge, $q$, and total mass, $m$, of the body go to zero, and $q/m$ goes to a well defined limit.
The Maxwell field $F_{ab}(\lambda)$ is assumed to be the retarded solution associated with $J^a(\lambda)$ plus a homogeneous solution (the "external field") that varies smoothly with $\lambda$.

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Then

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A. I. Harte, arXiv:0903.0167 (2009)
Original
2009
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