Instability of scalar charges in 1+1D and 2+1D

TL;DR

This paper investigates the instability of scalar charges in lower-dimensional flat spacetimes, revealing they lose mass via monopole radiation, unlike in the standard 3+1 dimensions.

Contribution

It demonstrates that scalar charges in 1+1D and 2+1D are unstable and emit monopole radiation, contrasting with their behavior in 3+1D.

Findings

Scalar charges in 1+1D and 2+1D lose mass through monopole radiation.

Such instability is absent in 3+1D scalar charges.

Lower-dimensional scalar charges are inherently unstable against self-interaction.

Abstract

We study the phenomenon of mass loss by a scalar charge -- a point particle which acts as a source for a (non-interacting) scalar field -- in (1+1)-dimensional and (2+1)-dimensional flat spacetime. We find that such particles are unstable against self interaction: they lose their mass through the emission of monopole radiation. This is in sharp contrast with scalar charges in (3+1)-dimensional flat spacetime, where no such phenomenon occurs.