Electromagnetic radiation in even-dimensional spacetimes

Abstract

The basic concepts and mathematical constructions of the Maxwell--Lorentz electrodynamics in flat spacetime of an arbitrary even dimension $d=2n$ are briefly reviewed. We show that the retarded field strength ${\mathcal{F}}_{\mu \nu }^{(2n)}$ due to a point charge living in a $2n$-dimensional world can be algebraically expressed in terms of the retarded vector potentials ${\mathcal{A}}_{\mu }^{(2m)}$ generated by this charge as if it were accommodated in $2m$-dimensional worlds nearby, $2\le m\le n+1$. With this finding, the rate of radiated energy-momentum of the electromagnetic field takes a compact form.

12 pages, no figures, this paper is dedicated to Prof. J. L. Buchbinder in celebration of his sixtieth birthday; v2: minor misprints are corrected, a further relevant reference is added

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• Electrodynamics in flat spacetime of six dimensions