Radiation reaction and renormalization in classical electrodynamics of a point particle in any dimension

Abstract

The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d = 4. For the cases of three and six dimensions the covariant analogs of the Lorentz-Dirac equation are explicitly derived.

Gravitational radiation inD-dimensional spacetimes

“…(22) tells us that the retarded Green's function for odd dimensions is non-zero inside the light cone. The consequence, as has been emphasized by different authors [19,22,24], is that for odd D the Huygens principle does not hold: the fact that the retarded Green's function support extends to the interior of the light cone implies the appearance of radiative tails in (16). In other words, we still have a propagation phenomenum for the wave equation in odd dimensional spacetimes, in so far as a localized initial state requires a certain time to reach a point in space.…”

Self-interaction and regularization of classical electrodynamics in higher dimensions

“…Following the technique introduced in [3] and [6] after changes = s + σ one can rewrite equation (14) as…”

“…For solving (6), on can make the Fourier transform of the whole equation. The resulting equation reads…”

“…Unfortunately, this technique fails already in eight dimensions, see [8]. Therefore, in order to come to higher dimensions, we apply here the method of expansion to series described in [6]. In the present paper the classical model of electro-dynamics with a single particle is considered in any even-dimensional space-time.…”

“…This leads to an infinite mass of the field. The problem of selfinteraction and regularization of corresponding infinities is considered in [6] in six dimensions. A receipt for obtaining the equations of motion based on rather general principles relating radiation and radiation friction is described in [7] in six-dimensional space-time.…”