Radiation reaction in various dimensions

TL;DR

This paper explores how radiation reaction behaves for an electric charge in various space-time dimensions, revealing that only in four dimensions does a local, consistent equation exist, while in others the behavior is non-local or divergent.

Contribution

It demonstrates that four dimensions uniquely allow a local radiation reaction equation with mass renormalization, unlike other dimensions where divergences or tail effects occur.

Findings

Four dimensions uniquely support a local differential equation for radiation reaction.

In odd dimensions, radiation reaction depends on the entire past history of the charge.

Divergences in higher even dimensions cannot be removed by mass renormalization.

Abstract

We discuss the radiation reaction problem for an electric charge moving in flat space-time of arbitrary dimensions. It is shown that four is the unique dimension where a local differential equation exists accounting for the radiation reaction and admitting a consistent mass-renormalization (the Dirac-Lorentz equation). In odd dimensions the Huygens principle does not hold; as a result, the radiation reaction force depends on the whole past history of a charge (radiative tail). We show that the divergence in the tail integral can be removed by the mass renormalization only in the 2+1 theory. In even dimensions higher than four, divergences can not be removed by a renormalization.