Electromagnetic radiation in even-dimensional spacetimes

TL;DR

This paper reviews Maxwell--Lorentz electrodynamics in even-dimensional flat spacetimes, deriving algebraic relations for retarded fields and presenting a compact expression for radiated energy-momentum.

Contribution

It introduces a novel algebraic expression for the retarded electromagnetic field in even dimensions and simplifies the calculation of radiated energy-momentum.

Findings

Retarded field strength can be expressed in terms of retarded potentials from nearby dimensions.

The energy-momentum radiation rate has a compact, simplified form.

The framework applies to arbitrary 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 ${\cal F}^{(2n)}_{\mu\nu}$ due to a point charge living in a $2n$-dimensional world can be algebraically expressed in terms of the retarded vector potentials ${\cal A}^{(2m)}_{\mu}$ 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.