Self-force and synchrotron radiation in odd space-time dimensions

TL;DR

This paper investigates the self-force and radiation reaction in odd-dimensional space-times, revealing that unlike in 3+1 dimensions, particles experience a non-zero self-force that aligns with radiation emission in 2+1 dimensions.

Contribution

It demonstrates that in odd-dimensional flat space-times, the self-force is non-zero and matches the radiation reaction, contrasting with the special case of 3+1 dimensions.

Findings

Self-force is non-zero in odd-dimensional space-times.

In 2+1 dimensions, self-force equals the radiation reaction force.

Classical electrodynamics behavior differs significantly in odd vs. even dimensions.

Abstract

Classical electrodynamics in flat 3+1 space-time has a very special retarded propagator delta(x^2) localized on the light cone, so that a particle does not interact with its past field. However, this is an exception, and in flat odd-dimensional space-times as well as generic curved spaces this is not so. In this work we show that the so called self-force is not only non-zero, but it matches (in 2+1 dimensions) the radiation reaction force derived from the radiation intensity.