Instability of scalar charges in 1+1D and 2+1D
  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. 
Lior M. Burko